Mensa IQ Test PDF | PDF - Free Printable

Let’s solve each question one by one, carefully and step by step.

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Question 1:
> The day before two days after the day before tomorrow is SATURDAY. What day is it today?

Let’s break this down backwards.

We’re told that “the day before two days after the day before tomorrow” = Saturday.

Let’s assign variables to make it easier.

Let “today” = X.

Then:
- “tomorrow” = X + 1
- “the day before tomorrow” = (X + 1) - 1 = X → so that’s just today
Wait — let’s re-read:

Actually:
“The day before two days after the day before tomorrow”

Break it from inside out:

Step 1: “the day before tomorrow” → that’s today

Step 2: “two days after [that]” → two days after today = day after tomorrow

Step 3: “the day before [that]” → the day before “day after tomorrow” = tomorrow

So the whole phrase simplifies to: “tomorrow” is Saturday

Therefore, if tomorrow is Saturday, then today is Friday.

✔ Check:
Today = Friday
Tomorrow = Saturday
Day before tomorrow = Friday
Two days after that = Sunday
Day before that = Saturday → matches!

Wait — hold on! Let me redo this more slowly.

Original:
“The day before two days after the day before tomorrow is SATURDAY.”

Let’s parse left to right with parentheses:

Let T = today

“the day before tomorrow” = T

“two days after [that]” = T + 2

“the day before [that]” = (T + 2) - 1 = T + 1

So: T + 1 = Saturday → Therefore, T = Friday.

Yes, same result.

But wait — let’s test with actual days.

Assume today is Friday.

Then:
- tomorrow = Saturday
- day before tomorrow = Friday
- two days after that = Sunday
- day before that = Saturday → YES! Matches.

So today is Friday.

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Question 2:
> What comes next, most logically, in the following sequence?
S A I B L C V D E E R F A G N H N I I J V K E L R M S N A O R
Options: a. PY b. BQ c. RR d. BR

This looks like a letter pattern. Let’s look for patterns.

First, write the letters with positions:

Position: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Letter: S A I B L C V D E E R F A G N H N I I J V K E L R M S N A O R

That’s 30 letters. We need to find what comes next — probably a pair of letters since options are pairs.

Maybe it’s alternating sequences? Or maybe every other letter forms a word?

Try splitting into two interleaved sequences:

Sequence 1 (odd positions): 1,3,5,7,... → S, I, L, V, E, R, A, N, N, I, V, E, R, S, A, R
→ S I L V E R A N N I V E R S A R → doesn’t spell anything obvious.

Sequence 2 (even positions): 2,4,6,8,... → A, B, C, D, E, F, G, H, I, J, K, L, M, N, O
→ A B C D E F G H I J K L M N O → That’s the alphabet! From A to O.

So even positions: A(2), B(4), C(6), D(8), E(10), F(12), G(14), H(16), I(18), J(20), K(22), L(24), M(26), N(28), O(30)

Next even position would be 32 → which should be P.

Now odd positions: Let’s list them again:

Pos 1: S
Pos 3: I
Pos 5: L
Pos 7: V
Pos 9: E
Pos 11: R
Pos 13: A
Pos 15: N
Pos 17: N
Pos 19: I
Pos 21: V
Pos 23: E
Pos 25: R
Pos 27: S
Pos 29: A

So: S, I, L, V, E, R, A, N, N, I, V, E, R, S, A

Hmm… “SILVER ANNIVERSARY”? Let’s see:

S I L V E R → SILVER
A N N I V E R S A R Y → but we have only up to A at pos 29.

After A at 29, next odd position is 31 → should be R? Then 33 → Y?

But the question asks for what comes next — and options are two-letter combos.

Since even positions go A to O (positions 2 to 30), next even is 32 → P

Odd positions: last was A at 29 → next odd is 31 → what should it be?

Looking at “SILVER ANNIVERSARY”:

S I L V E R A N N I V E R S A R Y

Positions:

1:S, 3:I, 5:L, 7:V, 9:E, 11:R → SILVER
13:A, 15:N, 17:N, 19:I, 21:V, 23:E, 25:R, 27:S, 29:A, 31:R, 33:Y → ANNIVERSARY

So at position 31 (next odd) should be R
At position 32 (next even) should be P

So next two letters: position 31 and 32 → R and P → but order?

The sequence is written as single letters, so next two letters in the full sequence would be:

Position 31: R (from odd sequence)
Position 32: P (from even sequence)

So the next two letters are R then P → "RP"? But that’s not an option.

Wait — the options are: a. PY b. BQ c. RR d. BR

None is RP.

Perhaps I got the order wrong.

The full sequence is given as a string: positions 1 to 30.

Next would be position 31 and 32.

If odd positions are 1,3,5,... and even are 2,4,6,...

Then position 31 is odd → part of first sequence → should be R (for ANNIVERSARY)

Position 32 is even → part of second sequence → should be P (after O)

So next two letters: 31=R, 32=P → so "RP"

But not in options.

Unless... maybe the answer is the pair for the next step, but perhaps they want the next pair as in the pattern of the options.

Another idea: maybe the sequence is grouped in pairs?

Look at the original: S A | I B | L C | V D | E E | R F | A G | N H | N I | I J | V K | E L | R M | S N | A O | R ?

Last is R at position 30, which is even? No, 30 is even, so it's the second letter of a pair.

Let’s group into pairs:

Pair 1: S A
Pair 2: I B
Pair 3: L C
Pair 4: V D
Pair 5: E E
Pair 6: R F
Pair 7: A G
Pair 8: N H
Pair 9: N I
Pair 10: I J
Pair 11: V K
Pair 12: E L
Pair 13: R M
Pair 14: S N
Pair 15: A O
Pair 16: R ?

Now look at first letters of pairs: S, I, L, V, E, R, A, N, N, I, V, E, R, S, A, R → same as before.

Second letters: A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, ?

Second letters: A,B,C,D,E,F,G,H,I,J,K,L,M,N,O → clearly alphabetical, so next should be P.

First letters: as before, spelling "SILVER ANNIVERSARY", so after A (pair 15), next is R (pair 16).

So pair 16: R and P → "RP"

Still not in options.

But option a is PY — close but not RP.

Perhaps I miscounted the word.

"SILVER ANNIVERSARY" has 15 letters? S-I-L-V-E-R-A-N-N-I-V-E-R-S-A-R-Y → 17 letters.

In our odd positions, we have 15 letters so far (up to pos 29: A), so next two odd positions: 31 and 33 should be R and Y.

But we need only the next two letters in the sequence, which are pos 31 and 32.

Pos 31: R (first letter of pair 16)
Pos 32: P (second letter of pair 16)

So "RP"

But not in options. Unless the answer is not RP.

Another thought: perhaps the second sequence is not continuing to P, but something else.

Or maybe the first sequence is not "ANNIVERSARY" but something else.

Let’s list the first letters again: positions 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29: S,I,L,V,E,R,A,N,N,I,V,E,R,S,A

That's 15 letters. "SILVER" is 6, "ANNIVERSARY" is 11, total 17, so we're missing two.

After A at 29, next should be R at 31, Y at 33.

But for the next pair, it's R and P.

Perhaps the options are for the next pair, and "PY" is a distractor.

But let's look at the options: a. PY b. BQ c. RR d. BR

None is RP.

Unless I have a mistake in the even sequence.

Even positions: 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30: A,B,C,D,E,F,G,H,I,J,K,L,M,N,O

Yes, A to O, 15 letters, next is P.

First letters: let's count how many we have for "SILVER ANNIVERSARY".

S I L V E R -> 6 letters (positions 1,3,5,7,9,11)

A N N I V E R S A R Y -> 11 letters, but we have only up to A at position 29, which is the 15th odd position.

Positions of odd indices: 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29 — that's 15 positions.

"SILVER" takes 6, so remaining 9 for "ANNIVERSARY", but "ANNIVERSARY" has 11 letters, so we have only "ANNIVERSA" or something.

Let's map:

After SILVER (6 letters), next is A (pos 13), N (15), N (17), I (19), V (21), E (23), R (25), S (27), A (29) — that's "ANNIVERSA" — 9 letters, so next should be R (31), Y (33).

So for pair 16: first letter R (pos 31), second letter P (pos 32) -> "RP"

But not in options.

Perhaps the sequence is different.

Another idea: maybe the second letters are not the alphabet, but something else.

Look at the pairs:

SA, IB, LC, VD, EE, RF, AG, NH, NI, IJ, VK, EL, RM, SN, AO, R?

Notice that in some pairs, the letters are related.

For example, SA: S and A — not obvious.

IB: I and B — I is 9th letter, B is 2nd.

LC: L=12, C=3

VD: V=22, D=4

EE: E=5, E=5

RF: R=18, F=6

AG: A=1, G=7

NH: N=14, H=8

NI: N=14, I=9

IJ: I=9, J=10

VK: V=22, K=11

EL: E=5, L=12

RM: R=18, M=13

SN: S=19, N=14

AO: A=1, O=15

R? : R=18, ?

Look at the second letter of each pair: A,B,C,D,E,F,G,H,I,J,K,L,M,N,O — yes, sequential from A to O.

So next second letter is P.

First letter of last pair is R, as per the word.

So "RP"

But since it's not in options, perhaps the answer is a. PY, assuming Y is for the word, but that would be later.

Maybe the next pair is for the completion, but the question says "what comes next", meaning the very next two letters.

Perhaps I need to see the pattern in the first letters.

List of first letters: S,I,L,V,E,R,A,N,N,I,V,E,R,S,A,R (assuming next is R)

Differences or something.

Another thought: perhaps the sequence is the letters of "SILVER ANNIVERSARY" interleaved with A to Z or something.

"SILVER ANNIVERSARY" has spaces, but in letters: S,I,L,V,E,R,A,N,N,I,V,E,R,S,A,R,Y — 17 letters.

Interleaved with A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z — but we have only 15 second letters so far.

In the sequence, there are 30 letters, so 15 pairs.

"SILVER ANNIVERSARY" is 17 letters, so it doesn't fit perfectly.

Perhaps it's "SILVER" and then "ANNIVERSARY" but cut off.

Let's count the letters in the given sequence for the first part.

From start: S A I B L C V D E E R F A G N H N I I J V K E L R M S N A O R

Let's try to read it as words.

Perhaps it's "SAILBCVDEERFAGNHNIIJVKELRMSNAOR" — not helpful.

Another idea: perhaps the sequence is two separate sequences combined, and the next is based on that.

We have even positions: A,B,C,D,E,F,G,H,I,J,K,L,M,N,O — so next is P.

Odd positions: S,I,L,V,E,R,A,N,N,I,V,E,R,S,A — let's see if this is a known sequence.

S to I: S is 19, I is 9 — difference -10

I to L: 9 to 12 +3

L to V: 12 to 22 +10

V to E: 22 to 5 -17

Not consistent.

Perhaps it's the letters of "SILVER" repeated or something.

Let's calculate the position in alphabet.

S=19, I=9, L=12, V=22, E=5, R=18, A=1, N=14, N=14, I=9, V=22, E=5, R=18, S=19, A=1

No obvious pattern.

Perhaps it's "SILVER" then "ANNIVERSARY" but we have only up to "ANNIVERSA", so next is R, then Y.

For the next pair, it should be R and P.

But since "RP" is not an option, and "PY" is, perhaps they mean the next two letters for the word, but that would be R and Y, not P and Y.

Unless the second sequence is not continuing.

Let's look at the last few pairs:

Pair 14: S N
Pair 15: A O
Pair 16: R ?

S N: S and N — S is 19, N is 14
A O: A=1, O=15
R ?: R=18, ?

If second letters are increasing by 1 each time: from A to O is +14 over 15 steps, so next +1 = P.

First letters: from S to A to R — not clear.

Perhaps the first letters are also following a pattern.

List of first letters of pairs: 1.S, 2.I, 3.L, 4.V, 5.E, 6.R, 7.A, 8.N, 9.N, 10.I, 11.V, 12.E, 13.R, 14.S, 15.A, 16.R

From 1 to 6: S,I,L,V,E,R — SILVER
7 to 15: A,N,N,I,V,E,R,S,A — ANNIVERSA
16: R — for ANNIVERSARY

So yes, next first letter is R.

Second letter is P.

So "RP"

But not in options. Perhaps the answer is c. RR, if they think the second letter is R, but that doesn't make sense.

Another possibility: perhaps the second sequence is not the alphabet, but the number of the pair or something.

Let's give up and look at the options. Maybe it's d. BR, but why.

Perhaps I misidentified the even sequence.

Let's list the second letters again: position 2:A, 4:B, 6:C, 8:D, 10:E, 12:F, 14:G, 16:H, 18:I, 20:J, 22:K, 24:L, 26:M, 28:N, 30:O — yes, A to O.

Next is P.

First letter of pair 16 is R.

So "RP"

Since it's not there, and "PY" is option a, perhaps they want the next two letters for the word "ANNIVERSARY", which would be R and Y, but Y is not P.

Unless the second sequence is different.

Let's check if the second letters correspond to something else.

In pair 1: S A — A is 1st letter
Pair 2: I B — B is 2nd
etc, so it's the nth letter of alphabet for the nth pair.

For pair 16, second letter should be the 16th letter, which is P.

First letter is R.

So "RP"

Perhaps the answer is not among the options, but that can't be.

Another idea: perhaps " what comes next" means the next item in the sequence of pairs, and the options are the pair, but maybe for a different reason.

Let's look at the last pair given: A O — which is pair 15.

Then next is pair 16: R and P.

But perhaps in the context, "R" is already given as the 30th letter? No, the 30th letter is R, which is the second letter of pair 15? Let's see.

The sequence is given as a string of 30 letters.

Position 30 is R, which is the second letter of pair 15? Pair 15 is positions 29 and 30: A and O? No.

Let's index properly.

The string is: let's write with indices.

1:S, 2:A, 3:I, 4:B, 5:L, 6:C, 7:V, 8:D, 9:E, 10:E, 11:R, 12:F, 13:A, 14:G, 15:N, 16:H, 17:N, 18:I, 19:I, 20:J, 21:V, 22:K, 23:E, 24:L, 25:R, 26:M, 27:S, 28:N, 29:A, 30:O, 31:R? Wait, the string ends with "A O R" — let's count the letters in the given sequence.

The sequence is: S A I B L C V D E E R F A G N H N I I J V K E L R M S N A O R

Let's count: 1S,2A,3I,4B,5L,6C,7V,8D,9E,10E,11R,12F,13A,14G,15N,16H,17N,18I,19I,20J,21V,22K,23E,24L,25R,26M,27S,28N,29A,30O,31R — oh! I think I missed that.

In the user's message, it's "S A I B L C V D E E R F A G N H N I I J V K E L R M S N A O R" — let's count the characters.

S,A,I,B,L,C,V,D,E,E,R,F,A,G,N,H,N,I,I,J,V,K,E,L,R,M,S,N,A,O,R — that's 31 letters? Let's list:

1. S
2. A
3. I
4. B
5. L
6. C
7. V
8. D
9. E
10. E
11. R
12. F
13. A
14. G
15. N
16. H
17. N
18. I
19. I
20. J
21. V
22. K
23. E
24. L
25. R
26. M
27. S
28. N
29. A
30. O
31. R

Oh! There are 31 letters, not 30. I miscounted earlier.

In the user's input: "S A I B L C V D E E R F A G N H N I I J V K E L R M S N A O R" — let's remove spaces: SAIBLCVDEERFAGNHNIIJVKELRMSNAOR — now count: S-A-I-B-L-C-V-D-E-E-R-F-A-G-N-H-N-I-I-J-V-K-E-L-R-M-S-N-A-O-R — that's 31 characters.

Yes, 31 letters.

So positions 1 to 31.

Now, even positions: 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30: A,B,C,D,E,F,G,H,I,J,K,L,M,N,O — 15 letters, A to O.

Next even position is 32, which should be P.

Odd positions: 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31: S,I,L,V,E,R,A,N,N,I,V,E,R,S,A,R

So: S,I,L,V,E,R,A,N,N,I,V,E,R,S,A,R — that's 16 letters.

"SILVER" is 6, "ANNIVERSARY" is 11, total 17, so we have "SILVER ANNIVERSAR" — missing Y.

So next odd position 33 should be Y.

But for the next two letters in the sequence, after position 31 (which is R), the next is position 32, which is even, so P.

So the next letter is P, but the question likely wants the next pair or something.

The sequence has 31 letters, so next is 32nd letter, which is P.

But the options are two-letter combinations, so perhaps they want the next two letters: 32 and 33.

Position 32: P (even sequence)
Position 33: Y (odd sequence, for "ANNIVERSARY")

So "PY"

And option a is PY.

Yes! That makes sense.

Because "SILVER ANNIVERSARY" requires Y at the end, and the even sequence continues to P.

So next two letters: P and Y → "PY"

Perfect.

So answer is a. PY

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Question 3:
> What is one twentieth of one half of one tenth of 10,000?

Let's compute step by step.

First, one tenth of 10,000 = 10,000 / 10 = 1,000

Then, one half of that = 1,000 / 2 = 500

Then, one twentieth of that = 500 / 20 = 25

Alternatively, multiply the fractions: (1/20) * (1/2) * (1/10) * 10,000 = (1/400) * 10,000 = 10,000 / 400 = 25

Yes.

So answer is 25.

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Question 4:
> What is the following scrambled word? NNREAIARYS

Let's unscramble it.

Letters: N,N,R,E,A,I,A,R,Y,S

Count: A:2, E:1, I:1, N:2, R:2, S:1, Y:1

Possible word: "ANNIVERSARY" — let's check: A,N,N,I,V,E,R,S,A,R,Y — but we have no V, and we have extra letters.

NNREAIARYS — 10 letters.

"ANNIVERSARY" is 11 letters.

Perhaps "ANNIVERSARY" without V? But that doesn't make sense.

List the letters: N,N,R,E,A,I,A,R,Y,S

Sort them: A,A,E,I,N,N,R,R,S,Y

Possible word: "ANNIVERSARY" has V, which is not here.

Another word: "RARY" or something.

Perhaps "ANNIVERSARY" is not it.

Let's try to form words.

Notice "ARY" at the end, "S" , "N", etc.

Perhaps "ANNIVERSARY" is intended, but missing V.

Count the letters in "NNREAIARYS": N,N,R,E,A,I,A,R,Y,S — that's 10 letters.

"ANNIVERSARY" is 11, so not.

Another common word: "ANNIVERSARY" might be misspelled, but let's think.

Perhaps "RARY" is part, but.

Let's try: start with A, then N, N, then I, V not there.

Perhaps it's "ANNIVERSARY" without the V, but that's not a word.

Another idea: perhaps it's "ANNIVERSARY" but the V is missing, or perhaps it's a different word.

Let's look for anagrams.

Letters: A,A,E,I,N,N,R,R,S,Y

Possible word: "ANNIVERSARY" requires V, not present.

"RARY" is not a word.

Perhaps "ANNIVERSARY" is not it; maybe "ANNIVERSARY" is 11 letters, but we have 10.

Count the scrambled word: "NNREAIARYS" — let's spell it: N-N-R-E-A-I-A-R-Y-S — 10 characters.

Perhaps it's "ANNIVERSARY" minus one letter, but which.

Another thought: perhaps it's "ANNIVERSARY" but with V omitted, but that doesn't help.

Let's try to rearrange.

Start with S, then A, then Y, etc.

S A Y — say

Then R, R, A, N, N, E, I

"Say" + "ran" + "rine" — not good.

"Anniversary" is close, but missing V.

Perhaps it's "ANNIVERSARY" and the V is implied, but unlikely.

Another word: "RARY" is not, but "RARY" could be part of "library" but no L.

Let's search for 10-letter words with these letters.

Perhaps "ANNIVERSARY" is not correct; maybe it's "ANNIVERSARY" but in the context, it's "ANNIVERSARY" and we have to ignore, but let's calculate the letters.

In question 2, we had "SILVER ANNIVERSARY", so likely this is "ANNIVERSARY".

But "ANNIVERSARY" has letters: A,N,N,I,V,E,R,S,A,R,Y — 11 letters.

Our scrambled word has 10 letters: N,N,R,E,A,I,A,R,Y,S — so missing V, and has an extra R or something.

Compare: "ANNIVERSARY" : A,N,N,I,V,E,R,S,A,R,Y — so letters: A:2, N:2, I:1, V:1, E:1, R:2, S:1, Y:1

Our scrambled: N,N,R,E,A,I,A,R,Y,S — so A:2, E:1, I:1, N:2, R:2, S:1, Y:1 — same as above but missing V.

So it's "ANNIVERSARY" without the V.

But that's not a word.

Perhaps it's a typo, and it's supposed to be "ANNIVERSARY" with V, but in the text, it's "NNREAIARYS", which has no V.

Another possibility: perhaps it's "ANNIVERSARY" but the V is represented by something else, but unlikely.

Let's try to unscramble as is.

Letters: A,A,E,I,N,N,R,R,S,Y

Possible word: "ANNIVERSARY" is not possible.

"RARY" is not.

"ANNIVERSARY" might be intended, and we should add V, but the instruction is to unscramble the given letters.

Perhaps it's "ANNIVERSARY" and the V is missing in the scramble, but that doesn't make sense.

Another idea: perhaps it's "ANNIVERSARY" but in the context of the previous question, but still.

Let's look for other words.

"Say" + "ran" + "rine" — not.

"Rain" + "years" — R,A,I,N,Y,E,A,R,S — that's 9 letters, we have 10.

With two N's and two R's.

"Anniversary" is the only logical choice, so perhaps it's "ANNIVERSARY" and we assume the V is there, but the scramble has 10 letters.

Count the letters in "NNREAIARYS": let's write it out: positions 1:N,2:N,3:R,4:E,5:A,6:I,7:A,8:R,9:Y,10:S — 10 letters.

Perhaps it's "ANNIVERSARY" without the first A or something.

"NNIVERSARY" — but that's not a word.

Perhaps it's "ANNIVERSARY" and the scramble is missing a letter, but for the sake of the problem, it's "ANNIVERSARY".

But let's try to form "ANNIVERSARY" with the letters: we have A,A,N,N,R,R,E,I,S,Y — missing V, so cannot.

Unless the V is included, but it's not in the string.

Another thought: in the scrambled word, "NNREAIARYS", perhaps "V" is not needed, but "ANNIVERSARY" requires V.

Perhaps it's "ANNIVERSARY" but in old English or something, but unlikely.

Let's consider that in question 2, we had "SILVER ANNIVERSARY", so likely this is "ANNIVERSARY", and perhaps the scramble has a mistake, or perhaps I need to include the V.

But the letters given are only those.

Perhaps "NNREAIARYS" can be unscrambled to "ANNIVERSARY" if we consider that "V" is not used, but that's impossible.

Let's try to see if there's a 10-letter word.

For example, "ANNIVERSARY" is 11, so perhaps "ANNIVERSAR" but not a word.

"RARY" is not.

Another idea: perhaps it's "ANNIVERSARY" and the scramble is for "ANNIVERSARY" but with V omitted by error, but for the problem, we should output "ANNIVERSARY".

But let's look at the letters: A,A,E,I,N,N,R,R,S,Y

Can we make "ANNIVERSARY" without V? No.

Perhaps "ANNIVERSARY" is not it; maybe "ANNIVERSARY" is for a different word.

Let's try "RARY" as in "library" but no L.

"Say" + "inner" + "ary" — S,A,Y,I,N,N,E,R,A,R,Y — but we have only one Y, and two A's, etc.

With our letters: A,A,E,I,N,N,R,R,S,Y

Let's try: S-A-Y- - then R-R-A-N-N-E-I

"Say" + "rann ei" not good.

"Rain" + "years" = R,A,I,N,Y,E,A,R,S — that's 9 letters, missing one N and one R? We have two N's and two R's, so "Rain years" would be R,A,I,N,Y,E,A,R,S — letters: A:2, E:1, I:1, N:1, R:2, S:1, Y:1 — but we have two N's, so not matching.

We have two N's, so "Rain" uses one N, need another.

"Annual" but no U.

Perhaps "Anniversary" is the intended answer, and we should box that.

Maybe it's "ANNIVERSARY" and the V is silent or something, but unlikely.

Another possibility: perhaps the scrambled word is "NNREAIARYS" and it's "ANNIVERSARY" with V missing, but in the context, it's accepted.

But let's calculate the number of letters: "ANNIVERSARY" has 11, we have 10, so not.

Unless the scramble includes all letters.

Let's double-check the user's input: "NNREAIARYS" — let's count the characters: N-N-R-E-A-I-A-R-Y-S — 10 characters.

Perhaps it's "ANNIVERSARY" and the first A is missing, but "NNIVERSARY" is not a word.

Perhaps it's "ANNIVERSARY" and we need to add V, but the instruction is to unscramble the given letters.

Let's try to unscramble to a different word.

For example, "RARY" is not, but "RARY" could be "rary" as in "summary" but no M,U.

"Say" + "ran" + "ire" + "y" — not.

"Years" + "rain" + "n" — Y,E,A,R,S,R,A,I,N,N — that's 10 letters: Y,E,A,R,S,R,A,I,N,N — which is exactly our letters: A,A,E,I,N,N,R,R,S,Y

Yes! So "Years rain n" not a word.

"Rain years n" not.

But "Anniversary" is not formed.

Perhaps "Anniversary" is not the word; maybe it's "Anniversary" but in the puzzle, it's "Anniversary" and we have to live with it.

Another idea: perhaps it's "ANNIVERSARY" and the V is represented by 'U' or something, but not.

Let's search online or think differently.

Perhaps it's "ANNIVERSARY" and the scramble has 'V' as 'U', but in the text, it's "NNREAIARYS", no U.

Let's look at the letters: A,A,E,I,N,N,R,R,S,Y

One possible word is "ANNIVERSARY" if we ignore the V, but that's not accurate.

Perhaps it's "ANNIVERSARY" for "anniversary", and in some contexts, but I think for the sake of time, since in question 2 it was "SILVER ANNIVERSARY", likely this is "ANNIVERSARY", so I'll go with that.

But to be precise, let's see if there's a 10-letter word.

Upon second thought, "ANNIVERSARY" can be spelled with 10 letters if we omit the V, but it's incorrect.

Perhaps the word is "ANNIVERSARY" and the scramble is missing a letter, but in the problem, it's given as is.

Another possibility: "NNREAIARYS" might be "ANNIVERSARY" with V replaced by nothing, but let's try to arrange as "A N N I V E R S A R Y" but no V.

Perhaps it's "ANNIVERSARY" and the 'V' is not in the scramble because it's a different word.

Let's try "RARY" as in "rary" but not.

"Say" + "inner" + "ary" — S,A,Y,I,N,N,E,R,A,R,Y — but we have only one Y, and this has two Y's? No, "say" has Y, "ary" has Y, so two Y's, but we have only one Y in the scramble.

Our scramble has one Y.

Letters: A:2, E:1, I:1, N:2, R:2, S:1, Y:1

So only one Y.

So "say" uses Y, "ary" would require another Y, not available.

"Year" + "s" + "rain" + "n" — Y,E,A,R,S,R,A,I,N,N — same as before.

Perhaps the word is "ANNIVERSARY" and we should output that.

I recall that in some puzzles, "ANNIVERSARY" is used, and perhaps here it's intended.

Maybe it's "ANNIVERSARY" and the scramble has a typo, but for now, I'll assume it's "ANNIVERSARY".

But let's try to see if "NNREAIARYS" can be "ANNIVERSARY" by adding V, but the instruction is to unscramble the given letters.

Perhaps the word is "ANNIVERSARY" and the 'V' is not needed because it's silent, but that's not true.

Another idea: perhaps it's "ANNIVERSARY" but in the context of the handout, it's "ANNIVERSARY", so I'll go with that.

So answer is ANNIVERSARY.

But to be accurate, let's notice that in the letters, we have all except V, so perhaps it's a mistake, but for the problem, we'll say ANNIVERSARY.

Perhaps it's "ANNIVERSARY" and the scramble is for "ANNIVERSARY" with V omitted, but in standard, it's with V.

Let's look for anagram solvers in mind.

With A,A,E,I,N,N,R,R,S,Y, one possible word is "ANNIVERSARY" if we had V, but without, perhaps "RARY" is not.

"Say" + "ran" + "rine" — not.

"Inner" + "years" + "a" — I,N,N,E,R,Y,E,A,R,S,A — but we have only one E, and this has two E's.

Our letters have only one E.

So not.

Perhaps "Anniversary" is the only logical choice, so I'll box that.

So for question 4, answer is ANNIVERSARY.

---

Question 5:
> In the following examples, each set of symbols stands for a word. Study all three words given and the symbol equivalent and translate the fourth line into a word.

Given:

First row: △ ○ ⊕ ⊕ △ → GREEN

Second row: △ ○ ▽ △ △ → GRASS

Third row: □□ ▽ ○ ⊗ △ → MARKS

Fourth row: □□ ⊕ △ △ ▽ → ?

We need to find what word this represents.

First, let's list the symbols and see which ones are common.

Symbols used: △, ○, ⊕, ▽, □□, ⊗

Note that □□ is probably a single symbol or two squares, but in the third row, it's "□□" which might be one unit.

In the fourth row, it's "□□" again, so likely a single symbol representing a letter or something.

Probably each symbol corresponds to a letter, and the sequence spells the word.

So for GREEN: 5 letters, and 5 symbols: △, ○, ⊕, ⊕, △

Similarly, GRASS: 5 letters, symbols: △, ○, ▽, △, △

MARKS: 5 letters, symbols: □□, ▽, ○, ⊗, △

Fourth: □□, ⊕, △, △, ▽ — 5 symbols, so 5-letter word.

Now, let's find which symbol corresponds to which letter.

First, compare GREEN and GRASS.

GREEN: △ ○ ⊕ ⊕ △

GRASS: △ ○ ▽ △ △

Both start with △ ○

GREEN ends with △, GRASS ends with △ △

Also, GREEN has ⊕ ⊕ in middle, GRASS has ▽ in third position.

Common letters: both have G,R,E,A,S but different.

GREEN: G,R,E,E,N

GRASS: G,R,A,S,S

So common first two letters: G and R.

In symbols, both have △ and ○ as first two symbols.

So likely △ = G, ○ = R

Then for GREEN: positions 3,4,5: ⊕, ⊕, △ → E,E,N

But △ is G, so last is G, but GREEN ends with N, not G. Contradiction.

GREEN is G,R,E,E,N — so fifth letter is N.

In symbols, fifth symbol is △, which we said is G, but should be N. Problem.

Perhaps △ is not G.

Let's list the mapping.

Let me denote the symbols:

Let A = △

B = ○

C = ⊕

D = ▽

E = □□ (since it's two squares, but treated as one symbol)

F = ⊗

So:

GREEN: A B C C A → G R E E N

GRASS: A B D A A → G R A S S

MARKS: E D B F A → M A R K S

Fourth: E C A A D → ?

From GREEN and GRASS, both start with A B, and both start with G R, so likely A=G, B=R

Then GREEN: A B C C A = G R E E N

So C C A = E E N

But A=G, so C C G = E E N, which implies G=N, contradiction unless G=N, but G and N are different.

So A cannot be G for both.

Perhaps the symbols represent the letters, but not necessarily in order, but the sequence is given, so likely in order.

Another idea: perhaps the symbols correspond to the letters, but we need to find which symbol is which letter by comparing.

From GREEN and GRASS:

GREEN: sym1=A, sym2=B, sym3=C, sym4=C, sym5=A → letters G,R,E,E,N

GRASS: sym1=A, sym2=B, sym3=D, sym4=A, sym5=A → letters G,R,A,S,S

So for position 1: both A, and both G, so A=G

Position 2: both B, both R, so B=R

Position 3: C for GREEN, D for GRASS; letters E for GREEN, A for GRASS

Position 4: C for GREEN, A for GRASS; letters E for GREEN, S for GRASS

Position 5: A for both, but letters N for GREEN, S for GRASS — conflict, since A cannot be both N and S.

So contradiction.

Unless the word is not spelled in order, but that doesn't make sense.

Perhaps the symbols represent the sound or something, but unlikely.

Another possibility: perhaps "□□" is not a single symbol, but two separate squares, but in the third row, it's "□□" and then other symbols, and in fourth "□□", so likely it's one unit.

In the third row: "□□ ▽ ○ ⊗ △" for MARKS, which is 5 letters, so 5 symbols, so "□□" is one symbol.

Similarly in fourth.

But in the conflict, for position 5, in GREEN it's A, letter N; in GRASS it's A, letter S; so A cannot be both.

Unless the mapping is not direct, or perhaps it's the number of strokes or something.

Let's look at the symbols visually.

△ triangle, ○ circle, ⊕ circle with cross, ▽ inverted triangle, □□ two squares, ⊗ circle with X.

Perhaps each symbol corresponds to a letter based on shape or something.

For example, △ might be A, since triangle looks like A.

○ might be O, circle.

⊕ might be Q or something.

But let's try.

Suppose △ = A

Then in GREEN: A B C C A = G R E E N, so if A=A, then first and last are A, but GREEN starts with G, ends with N, not A.

Not good.

Suppose △ = G

Then GREEN: G B C C G = G R E E N, so B=R, C C G = E E N, so C=E, and G=N, contradiction.

Same issue.

Perhaps the symbols are for the letters, but the word is coded, and we need to find the code.

From GREEN and GRASS, both have A B at start, and G R at start, so A=G, B=R.

Then for GREEN: positions 3,4,5: C,C,A = E,E,N

For GRASS: positions 3,4,5: D,A,A = A,S,S

So from GREEN: C,C,A = E,E,N

From GRASS: D,A,A = A,S,S

So from GRASS, A,A = S,S, so A=S

But from earlier, A=G, so G=S, contradiction.

From GRASS: D,A,A = A,S,S, so the last two A,A correspond to S,S, so A=S

From GREEN: C,C,A = E,E,N, and A=S, so C,C,S = E,E,N, so C=E, and S=N, contradiction.

So impossible if we assume the symbols map directly to letters in order.

Perhaps the symbols represent the letter by its position or something.

Another idea: perhaps the number of lines or something.

Let's list the symbols and their properties.

△ : 3 lines

○ : 1 line (circle)

⊕ : circle with cross, so perhaps 2 lines or 4

▽ : 3 lines, inverted

□□ : two squares, each square has 4 lines, but together, perhaps 8 or 4 if shared, but likely 8 lines or something.

This might be complicated.

Perhaps each symbol corresponds to a letter based on the shape resembling the letter.

For example, △ looks like A

○ looks like O

⊕ looks like Q or O with plus

▽ looks like V or A inverted

□□ looks like H or something

⊗ looks like X

Let's try that.

Suppose:

△ = A (triangle)

○ = O (circle)

⊕ = Q (circle with cross)

▽ = V (inverted triangle)

□□ = H (two squares side by side might look like H)

⊗ = X (circle with X)

Now check GREEN: △ ○ ⊕ ⊕ △ = A O Q Q A

But GREEN is G R E E N, not matching.

GRASS: △ ○ ▽ △ △ = A O V A A, not G R A S S.

Not good.

Perhaps different mapping.

Another idea: perhaps the symbols represent the letter by the number of enclosed regions or something.

For example, ○ has 1 enclosed region

△ has 0

⊕ has 1 ( the circle) or 4 if count the crosses, but usually in such puzzles, ⊕ has 1 enclosed region ( the circle)

▽ has 0

□□ has 2 enclosed regions ( two squares)

⊗ has 1 enclosed region ( the circle)

Let's define:

Let E = number of enclosed regions.

△ : 0

○ : 1

⊕ : 1 (assuming the circle is enclosed, the cross doesn't add)

▽ : 0

□□ : 2 ( two separate squares)

⊗ : 1 ( the circle)

Now for GREEN: symbols: △(0), ○(1), ⊕(1), ⊕(1), △(0) → 0,1,1,1,0

Letters: G,R,E,E,N

What do these numbers correspond to? Perhaps the number of enclosed regions in the letter.

G: has 1 enclosed region? G has one enclosed region if written with a loop, but usually G has one.

Standard: A has 1, B has 2, C has 0, D has 1, E has 0, F has 0, G has 1, H has 0, I has 0, J has 0, K has 0, L has 0, M has 0, N has 0, O has 1, P has 1, Q has 1, R has 1, S has 0, T has 0, U has 0, V has 0, W has 0, X has 0, Y has 0, Z has 0.

G: typically has 1 enclosed region ( the bowl)

R: has 1 ( the bowl)

E: has 0

N: has 0

So GREEN: G:1, R:1, E:0, E:0, N:0 → 1,1,0,0,0

But symbols give 0,1,1,1,0 — not match.

GRASS: G:1, R:1, A:1, S:0, S:0 → 1,1,1,0,0

Symbols: △(0), ○(1), ▽(0), △(0), △(0) → 0,1,0,0,0 — not match.

Not good.

Perhaps the sum or something.

Another approach: let's look at the common symbols.

From GREEN and GRASS, both have △ and ○ in first two positions, and both words start with G and R, so likely △=G, ○=R.

Then for GREEN: positions 3,4,5: ⊕, ⊕, △ = E,E,N

But △=G, so ⊕, ⊕, G = E,E,N, so ⊕=E, and G=N, impossible.

Unless the last symbol is not for the last letter, but that doesn't make sense.

Perhaps the word is reversed or something.

Let's try reversing the symbol sequence.

For GREEN: if we reverse the symbols: △ ⊕ ⊕ ○ △ → N E E R G, which is not GREEN.

Not good.

Another idea: perhaps the symbols represent the letter by its alphabetical position modulo something.

Let's list the letters and see.

Perhaps from the three words, we can find which symbol is which letter by elimination.

Let me make a table.

Let S1 = △, S2 = ○, S3 = ⊕, S4 = ▽, S5 = □□, S6 = ⊗

Words:

GREEN: S1,S2,S3,S3,S1

GRASS: S1,S2,S4,S1,S1

MARKS: S5,S4,S2,S6,S1

Fourth: S5,S3,S1,S1,S4

Now, from GREEN and GRASS, both have S1,S2 at start, and both start with G,R, so S1=G, S2=R

Then GREEN: S1,S2,S3,S3,S1 = G,R,?,?,G but should be G,R,E,E,N, so the last is G, but should be N, so unless N=G, not.

Perhaps S1 is not G for the last position.

In GREEN, S1 is first and last, letters G and N, so S1 cannot be both G and N.

So the only way is if the mapping is not one-to-one, or perhaps it's the sound, but unlikely.

Perhaps the symbols represent the letter by the number of strokes to write it.

For example, G: 1 stroke or 2, depending.

This is messy.

Let's look at MARKS: S5,S4,S2,S6,S1 = M,A,R,K,S

And we have S2=R from earlier assumption.

So S2=R

Then MARKS: S5,S4,R,S6,S1 = M,A,R,K,S

So S5=M, S4=A, S6=K, S1=S

But from earlier, S1=G from GREEN and GRASS, but now S1=S, contradiction.

From MARKS, if S2=R, then S5,S4,R,S6,S1 = M,A,R,K,S, so S5=M, S4=A, S6=K, S1=S

From GREEN: S1,S2,S3,S3,S1 = S,R,?,?,S = G,R,E,E,N, so S=G and S=N, impossible.

So S1 cannot be both S and G.

Unless in GREEN, S1 is G for first, but for last, it's N, so not the same.

Perhaps the symbol S1 represents different letters in different contexts, but that doesn't make sense for a code.

Another idea: perhaps the symbols are for the letters, but the word is coded with a cipher, like each symbol corresponds to a letter, but we need to find the mapping from the examples.

Let's list all symbol occurrences.

From GREEN: S1 appears twice, S2 once, S3 twice

Letters: G once, R once, E twice, N once — so S3 corresponds to E, since it appears twice, and E appears twice.

S1 appears twice, but G and N are different, so not.

In GREEN, S1 is at position 1 and 5, letters G and N, so not the same letter.

So S1 does not always represent the same letter, which is strange for a code.

Unless it's not a substitution cipher.

Perhaps the symbols represent the shape of the letter or something else.

Let's look at the fourth row: □□ ⊕ △ △ ▽

And we need to find the word.

From the third row, □□ ▽ ○ ⊗ △ = MARKS

So if we can find what each symbol means.

Assume that each symbol corresponds to a specific letter.

From MARKS: let's say P1=□□, P2=▽, P3=○, P4=⊗, P5=△ = M,A,R,K,S

So P1=M, P2=A, P3=R, P4=K, P5=S

Now check with GREEN: △ ○ ⊕ ⊕ △ = P5, P3, ?, ?, P5 = S, R, ?, ?, S

But GREEN is G,R,E,E,N, so S,R,?,?,S = G,R,E,E,N, so S=G and S=N, impossible.

Same issue.

Unless for GREEN, it's not the same mapping.

Perhaps the symbols are consistent, but the word is different.

Another thought: perhaps "GREEN" is not the word, but the color, but the symbols represent the letters of the word.

I think I need to consider that in GREEN, the last symbol is △, which is S from MARKS, but in GREEN it should be N, so not.

Let's list the symbols for each word:

For GREEN: symbols: T, C, P, P, T (using T for triangle, C for circle, P for plus-circle, etc.)

Perhaps use abbreviations.

Let Tr = △, Ci = ○, Pl = ⊕, In = ▽, Sq = □□, Cr = ⊗

So:

GREEN: Tr, Ci, Pl, Pl, Tr

GRASS: Tr, Ci, In, Tr, Tr

MARKS: Sq, In, Ci, Cr, Tr

Fourth: Sq, Pl, Tr, Tr, In

Now, notice that in GRASS and GREEN, both have Tr, Ci at start.

In MARKS, Ci is third, Tr is last.

Also, in GRASS, In is third, in MARKS, In is second.

Let's see what letter is common.

For example, the letter 'R' appears in all three words: GREEN has R, GRASS has R, MARKS has R.

In GREEN, R is second letter, symbol Ci

In GRASS, R is second letter, symbol Ci

In MARKS, R is third letter, symbol Ci

Oh! In all cases, when R is in the word, it is represented by Ci (○)

In GREEN: position 2: R, symbol Ci

In GRASS: position 2: R, symbol Ci

In MARKS: position 3: R, symbol Ci

So consistently, Ci = R

Great!

Similarly, let's find other letters.

Look at 'A': in GRASS, A is third letter, symbol In

In MARKS, A is second letter, symbol In

So In = A

Because in GRASS: position 3: A, symbol In

In MARKS: position 2: A, symbol In

So In = A

Now, 'S': in GRASS, S is fourth and fifth letter, symbols Tr and Tr

In MARKS, S is fifth letter, symbol Tr

So Tr = S

Because in GRASS: positions 4 and 5: S,S, symbols Tr,Tr

In MARKS: position 5: S, symbol Tr

So Tr = S

Now, 'G': in GREEN, G is first letter, symbol Tr

But Tr = S, and G is not S, contradiction.

In GREEN, first letter G, symbol Tr, but we have Tr = S, so G=S, not true.

Problem.

In GREEN, first symbol Tr, letter G

But from above, Tr = S, so G=S, impossible.

Unless in GREEN, the first symbol is for G, but Tr is S, so not.

Perhaps for GREEN, the first symbol is Tr, which is S, but G is not S.

So conflict.

Let's list what we have.

From above:

Ci = R (from all three words)

In = A ( from GRASS and MARKS)

Tr = S ( from GRASS and MARKS)

Now for GREEN: symbols: Tr, Ci, Pl, Pl, Tr = S, R, Pl, Pl, S

But GREEN is G,R,E,E,N, so S,R,Pl,Pl,S = G,R,E,E,N

So S=G and S=N, impossible.

So the only way is if Pl corresponds to E, and S corresponds to G and N, which is not possible.

Perhaps the word "GREEN" has S at the end, but it's N.

Another idea: perhaps the symbols represent the letter by its initial sound or something, but G and S are different.

Let's look at the fourth symbol in GREEN: Pl, and it's E, so Pl = E

Then from GREEN: S,R,E,E,S = G,R,E,E,N, so S=G and S=N, still contradiction.

Unless the last S is for N, but S is not N.

Perhaps in the code, the symbol Tr represents different letters, but that doesn't make sense.

Let's check the third word MARKS: Sq, In, Ci, Cr, Tr = Sq, A, R, Cr, S = M,A,R,K,S

So Sq = M, Cr = K

Good.

Now for GRASS: Tr, Ci, In, Tr, Tr = S, R, A, S, S = G,R,A,S,S

So S,R,A,S,S = G,R,A,S,S, so the first S should be G, but S is not G.

So for the first position, in GRASS, symbol Tr = S, but letter is G, so not match.

Unless the mapping is not for the letter, but for the position or something.

Perhaps the symbols indicate the letter by the number of the symbol in a list, but complicated.

Another thought: perhaps the symbols are to be interpreted as the letter they resemble, and for Tr, it might be A, but in MARKS, Tr is S, not A.

In MARKS, Tr is last, S, and S does not resemble triangle.

Perhaps for each word, the symbols are mapped based on the word, but that doesn't help for decoding.

Let's look at the fourth row: Sq, Pl, Tr, Tr, In

From above, we have In = A, Tr = S, Sq = M, and Pl is unknown.

From GREEN, Pl is used for E, so perhaps Pl = E

Then fourth row: Sq, Pl, Tr, Tr, In = M, E, S, S, A

So "MESSA" which is not a word, but "MESSAGE" is 7 letters, not 5.

"MESSA" could be "massa" but not common.

Perhaps "ASSES" but M E S S A.

Not a word.

"MASSE" is a word, but usually not.

Perhaps it's "ASSESS" but 6 letters.

Another idea: perhaps "Sq" is not M, but in MARKS, Sq is first, M, so likely M.

Let's list the letters we have.

From MARKS: Sq = M, In = A, Ci = R, Cr = K, Tr = S

From GRASS: Tr = S, Ci = R, In = A, and Tr, Tr for S,S, good, but first Tr for G, but Tr=S, so G should be S, not.

Unless in GRASS, the first letter G is represented by Tr, but Tr is S, so perhaps G is coded as S, but that doesn't make sense.

Perhaps the code is that the symbol represents the letter that has the same number of enclosed regions or something.

Let's calculate the number of enclosed regions for the letters.

As before:

G: 1 ( if written with a loop)

R: 1

E: 0

N: 0

For GREEN: letters G:1, R:1, E:0, E:0, N:0

Symbols: Tr:0 (triangle has no enclosed region), Ci:1 (circle has 1), Pl:1 (circle with cross, still 1 enclosed region), Pl:1, Tr:0

So symbols: 0,1,1,1,0

Letters: 1,1,0,0,0 — not match.

For GRASS: G:1, R:1, A:1, S:0, S:0 → 1,1,1,0,0

Symbols: Tr:0, Ci:1, In:0 (inverted triangle, no enclosed), Tr:0, Tr:0 → 0,1,0,0,0 — not match.

For MARKS: M:0, A:1, R:1, K:0, S:0 → 0,1,1,0,0

Symbols: Sq:2 ( two squares, each has 1 enclosed, so 2), In:0, Ci:1, Cr:1 (circle with X, still 1 enclosed), Tr:0 → 2,0,1,1,0 — not match.

Not good.

Perhaps the sum of enclosed regions.

For GREEN: letters sum 1+1+0+0+0=2, symbols 0+1+1+1+0=3, not match.

Another idea: perhaps the symbols represent the letter by the number of lines in the symbol.

Tr: 3 lines

Ci: 1 line (circle)

Pl: 2 lines ( the cross) or 4, but usually in such puzzles, ⊕ is considered to have 2 lines for the cross, but the circle is curved, so perhaps not.

Assume:

Tr: 3

Ci: 1 ( circumference)

Pl: 2 ( the two lines of the cross)

In: 3

Sq: 8 ( two squares, 4 each)

Cr: 2 ( the two lines of the X)

Then for GREEN: 3,1,2,2,3 = G,R,E,E,N

What numbers for letters? G:7, R:18, etc, not matching.

Perhaps the number corresponds to the letter position.

G=7, R=18, E=5, N=14

Symbols: 3,1,2,2,3 — not match.

Not good.

Let's go back to the consistent mapping we had.

From the three words, we have that Ci = R, because in all cases where R appears, it is represented by Ci.

In GREEN: R is second, symbol Ci

In GRASS: R is second, symbol Ci

In MARKS: R is third, symbol Ci

So Ci = R

Similarly, In = A, because in GRASS: A is third, symbol In; in MARKS: A is second, symbol In

So In = A

Tr = S, because in GRASS: S is fourth and fifth, symbols Tr,Tr; in MARKS: S is fifth, symbol Tr

So Tr = S

Now for GREEN: symbols: Tr, Ci, Pl, Pl, Tr = S, R, Pl, Pl, S

Letters: G, R, E, E, N

So S, R, Pl, Pl, S = G, R, E, E, N

Therefore, S = G and S = N, which is impossible unless G=N=S, not true.

The only resolution is that for the first and last positions, the symbol Tr represents different letters, but that violates the code.

Perhaps in GREEN, the last symbol is for N, but Tr is S, so not.

Another possibility: perhaps "GREEN" is misspelled or something, but unlikely.

Let's look at the fourth symbol in GREEN: Pl, and it's E, so Pl = E

Then for the first symbol, Tr = S, but should be G, so perhaps G is coded as S, but why.

Perhaps the code is that the symbol represents the letter that is k positions away, but complicated.

Let's notice that in GRASS, the first letter G is represented by Tr, and Tr = S, so G is coded as S.

In GREEN, G is coded as Tr = S, so G->S

In MARKS, no G, so ok.

Then for N in GREEN, last symbol Tr = S, so N->S

So both G and N are coded as S.

Then for E, Pl = E, so E->E

R->R

So the code is: G->S, R->R, E->E, N->S, A->A, etc.

Then for GRASS: G->S, R->R, A->A, S->S, S->S, so symbols: S,R,A,S,S which matches Tr,Ci,In,Tr,Tr since Tr=S, Ci=R, In=A

For MARKS: M->?, A->A, R->R, K->?, S->S

Symbols: Sq, In, Ci, Cr, Tr = Sq, A, R, Cr, S

Letters: M,A,R,K,S

So Sq = M, Cr = K, and M->M, K->K, so no change for M and K.

For GREEN: G->S, R->R, E->E, E->E, N->S, so symbols: S,R,E,E,S which is Tr,Ci,Pl,Pl,Tr, and Pl=E, so yes, matches.

Perfect! So the code is that some letters are mapped to other letters: specifically, G and N are both mapped to S, while others are mapped to themselves.

In this case, for the words given, G and N are coded as S, and other letters are coded as themselves.

So the mapping is:

G -> S

N -> S

R -> R

E -> E

A -> A

M -> M

K -> K

S -> S

etc.

Now for the fourth row: symbols: Sq, Pl, Tr, Tr, In

From above, Sq = M (from MARKS, and M->M)

Pl = E (from GREEN, E->E)

Tr = S (and S->S, or G->S, N->S, but here it's S)

In = A (A->A)

So symbols: Sq= M, Pl= E, Tr= S, Tr= S, In= A

So the coded letters are: M, E, S, S, A

But since the code maps G and N to S, but here the letters are M,E,S,S,A, and S is already S, so the actual word is M,E,S,S,A — "MESSA" which is not a word, but perhaps "MASSE" or "ASSESS" but not.

The coded sequence is M,E,S,S,A, and since the code is applied to the original word to get the symbols, so to decode, we need to reverse the mapping.

The mapping is: when encoding, G and N are replaced by S, other letters unchanged.

So for decoding, when we see S, it could be G, N, or S.

In the coded sequence for the fourth row: M,E,S,S,A

So the original word has letters: for M, since M->M, so original M

E->E, so E

S-> could be G, N, or S

S-> could be G, N, or S

A->A, so A

So possible words: M,E,G,G,A or M,E,G,N,A or M,E,N,G,A or M,E,N,N,A or M,E,S,G,A etc.

We need a 5-letter word that makes sense.

Possible words: "MENGA" not, "MENG A" not.

"MESSAGE" is 7 letters.

"ASSES" is 5 letters, but starts with A.

"MASSE" is a word, meaning mass in French, but in English, "masse" is not common.

"ASSESS" is 6 letters.

Another possibility: "GENES" but not matching.

Perhaps "SAGES" but not.

Let's list possible combinations.

The coded letters are M,E,S,S,A

Decoded: first letter M (since M->M)

Second E (E->E)

Third S -> could be G,N,S

Fourth S -> G,N,S

Fifth A (A->A)

So possible original words: M,E,G,G,A — "MEGGA" not a word

M,E,G,N,A — "MEGNA" not

M,E,G,S,A — "MEGSA" not

M,E,N,G,A — "MENGA" not

M,E,N,N,A — "MENNA" not

M,E,N,S,A — "MENSA" — oh! "MENSA" is a word, the high IQ society.

M,E,N,S,A

And in the code, N->S, S->S, so for "MENSA": M->M, E->E, N->S, S->S, A->A, so coded as M,E,S,S,A which matches the symbols Sq,Pl,Tr,Tr,In

Perfect!

So the word is MENSA.

And it makes sense in the context of an intelligence test handout.

So for question 5, answer is MENSA.

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Question 6:
> Which of the sentences given below means approximately the same as: “Beauty is only skin deep”?

Options:
a. Some actresses are made up by the studios so that you cannot tell what they really look like.
b. Don't judge a book by its cover.
c. Some people have prettier appearances than others.
d. Good looks don't matter that much.

“Beauty is only skin deep” means that physical beauty is superficial and not important compared to inner qualities.

So we need a sentence that conveys that appearance is not everything, or that we should not value looks too much.

Option a: talks about actresses being made up, which is about deception in appearance, but not directly about the depth of beauty.

Option b: "Don't judge a book by its cover." This means don't judge something by its outward appearance, which is very similar to "beauty is only skin deep" — both suggest that外表 is not indicative of true value.

Option c: states that some people are prettier, which is factual but doesn't address the depth or importance.

Option d: "Good looks don't matter that much." This is close, as it says looks are not important, which is implied by "only skin deep".

But "beauty is only skin deep" emphasizes that beauty is shallow, not that it doesn't matter, though it implies that inner qualities are more important.

Option b is a common proverb that directly parallels the idea: just as a book's cover doesn't reflect its content, a person's beauty doesn't reflect their character.

Option d is also good, but "don't matter that much" might be stronger than "only skin deep", which allows that beauty exists but is superficial.

In common usage, "beauty is only skin deep" is often paired with "don't judge a book by its cover" as similar sayings.

Moreover, option b is a direct analogy.

So likely b is the best answer.

To confirm, let's see the meanings.

“Beauty is only skin deep”: Physical attractiveness is superficial and not a reflection of inner worth.

b. "Don't judge a book by its cover": Do not evaluate something based solely on its outward appearance.

Very similar.

d. "Good looks don't matter that much": This says looks are unimportant, which is a consequence, but the original saying is about the nature of beauty being shallow, not necessarily that it doesn't matter.

But in practice, both are used similarly.

However, b is more precise because it's about judgment based on appearance, which is the core of the saying.

Also, in many sources, these two proverbs are considered synonymous.

So I think b is the answer.

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Now, to summarize the answers:

1. Friday

2. a. PY

3. 25

4. ANNIVERSARY (despite the letter count issue, it's the intended word)

5. MENSA

6. b. Don't judge a book by its cover.

For question 4, upon second thought, with the letters N,N,R,E,A,I,A,R,Y,S, we can form "ANNIVERSARY" if we consider that 'V' is missing, but actually, "ANNIVERSARY" requires V, so perhaps it's a different word.

Let's try to unscramble "NNREAIARYS" to a 10-letter word.

Letters: A,A,E,I,N,N,R,R,S,Y

One possible word is "ANNIVERSARY" without V, but not.

"RARY" is not.

"Say" + "ran" + "ire" + "y" — not.

"Years" + "rain" + "n" — Y,E,A,R,S,R,A,I,N,N — which is "years rain n" not a word.

But "ANNIVERSARY" is 11 letters, so perhaps the scramble has 11 letters, but in the text, it's "NNREAIARYS" which is 10.

Perhaps it's "ANNIVERSARY" and the first 'A' is missing, but "NNIVERSARY" is not a word.

Another idea: perhaps it's "ANNIVERSARY" and the 'V' is represented by 'U', but not in letters.

Let's count the letters in "NNREAIARYS": N-N-R-E-A-I-A-R-Y-S — 10 characters.

Perhaps it's "ANNIVERSARY" for "anniversary", and in the context, we accept it.

Maybe it's "ANNIVERSARY" and the scramble is "NNREAIARYS" which can be rearranged to "ANNIVERSARY" by adding V, but the instruction is to unscramble the given letters.

Upon searching my memory, I recall that "ANNIVERSARY" can be anagrammed, but with these letters, one possible word is "ANNIVERSARY" if we had V, but without, perhaps "RARY" is not.

Let's try: start with A, then N, N, then I, then V not there.

Perhaps it's "ANNIVERSARY" and the 'V' is omitted in the scramble by error, but for the problem, we'll go with ANNIVERSARY.

So I'll keep that.

Final answers:

1. Friday

2. a. PY

3. 25

4. ANNIVERSARY

5. MENSA

6. b

Now for the response.