Math worksheet for practicing double-digit multiplication with a fun puzzle element.

Let's solve this step-by-step.

We are given a set of multiplication problems involving double-digit numbers. Each problem has an answer, and each answer corresponds to a letter. We need to:

1. Solve each multiplication problem.
2. Match the answer to the corresponding letter.
3. Fill in the boxes with the correct letters based on the answers.
4. Reveal the hidden message.

---

Step 1: Solve Each Multiplication Problem

We'll go through each one.

---

#### 1. 50 × 33
```
50
× 33
-----
150 ← 50 × 3
150 ← 50 × 30 (shifted)
-----
1,650
```
✔ Answer: 1,650 → Letter: N

---

#### 2. 25 × 16
```
25
× 16
-----
150 ← 25 × 6
250 ← 25 × 10 (shifted)
-----
400
```
✔ Answer: 400 → Letter: T? Wait — let’s check the key.

Looking at the bottom, we see:
- 400 → A (from 67 × 21)

Wait — no. Let's look carefully.

Actually, the letters are assigned below the problems.

So for each problem, the answer is matched to a letter.

From the worksheet:

- 1,650 → N ✔
- 400 → A ✔ (from 67 × 21)
- But we need to match each product to its assigned letter.

Let’s list all the problems and their products, then find which letter goes with which product.

---

List All Problems & Their Answers

1. 50 × 33 = 1,650 → N (already given)

2. 25 × 16
```
25 × 16 = (20 + 5) × 16 = 320 + 80 = 400
```
✔ 400 → A? Wait — but look at the key.

Wait — the letters are shown below the problems.

Let’s read the layout:

Each problem has a blank line underneath it, and then a box with a letter.

For example:
- 50 × 33 → 1,650 → N
- 25 × 16 → ___ → L
- 71 × 20 → ___ → M
- 46 × 19 → ___ → E
- 30 × 30 → ___ → T
- 22 × 25 → ___ → R
- 45 × 11 → ___ → S
- 83 × 10 → ___ → O
- 67 × 21 → ___ → A
- 78 × 15 → ___ → B
- 59 × 26 → ___ → U

So the letters are already assigned to each problem.

But we need to compute the products and use them to fill in the boxes at the top.

The top has several sets of boxes with numbers underneath:

```
[ ] [ ] N [ ] [ ] [ ] [ ] [ ] N
495 1,534 1,650 495 874 900 495 830 1,650

[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]
1,420 1,407 550 495 1,407 550 874 1,170 400 1,534 874
```

So we need to compute all the products, then place the letter associated with that product into any box where the number matches.

Let’s compute all the multiplication problems.

---

Compute Each Product

1. 50 × 33 = 1,650 → N

2. 25 × 16
= 25 × (10 + 6) = 250 + 150 = 400 → L

3. 71 × 20
= 71 × 2 × 10 = 142 × 10 = 1,420 → M

4. 46 × 19
Use distributive property:
= 46 × (20 - 1) = 920 - 46 = 874 → E

5. 30 × 30 = 900 → T

6. 22 × 25
= (20 + 2) × 25 = 500 + 50 = 550 → R

7. 45 × 11
= 45 × (10 + 1) = 450 + 45 = 495 → S

8. 83 × 10 = 830 → O

9. 67 × 21
= 67 × (20 + 1) = 1,340 + 67 = 1,407 → A

10. 78 × 15
= 78 × (10 + 5) = 780 + 390 = 1,170 → B

11. 59 × 26
= (60 - 1) × 26 = 60×26 - 26 = 1,560 - 26 = 1,534 → U

---

Summary of Products and Letters

| Problem | Product | Letter |
|--------|--------|--------|
| 50×33 | 1,650 | N |
| 25×16 | 400 | L |
| 71×20 | 1,420 | M |
| 46×19 | 874 | E |
| 30×30 | 900 | T |
| 22×25 | 550 | R |
| 45×11 | 495 | S |
| 83×10 | 830 | O |
| 67×21 | 1,407 | A |
| 78×15 | 1,170 | B |
| 59×26 | 1,534 | U |

Now, let’s go to the top boxes.

We have these numbers under the boxes:

#### First row:
Boxes: [ ] [ ] N [ ] [ ] [ ] [ ] [ ] N
Numbers: 495 1,534 1,650 495 874 900 495 830 1,650

So we need to place letters that correspond to those numbers.

Let’s do each number:

- 495 → from 45×11 → S
- 1,534 → from 59×26 → U
- 1,650 → from 50×33 → N
- 874 → from 46×19 → E
- 900 → from 30×30 → T

So fill in:

First row:

- First box: 495 → S
- Second box: 1,534 → U
- Third box: 1,650 → N (already given)
- Fourth box: 495 → S
- Fifth box: 874 → E
- Sixth box: 900 → T
- Seventh box: 495 → S
- Eighth box: 830 → from 83×10 → O
- Ninth box: 1,650 → N

So first row becomes:

S U N S E T O N

Wait — let's write it clearly:

Box 1: 495 → S
Box 2: 1,534 → U
Box 3: 1,650 → N
Box 4: 495 → S
Box 5: 874 → E
Box 6: 900 → T
Box 7: 495 → S
Box 8: 830 → O
Box 9: 1,650 → N

So: S U N S E T O N

That looks like "SUNSET ON" — maybe part of a sentence?

Now second row:

[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]

Numbers: 1,420 1,407 550 495 1,407 550 874 1,170 400 1,534 874

Now assign letters:

- 1,420 → 71×20 → M
- 1,407 → 67×21 → A
- 550 → 22×25 → R
- 495 → 45×11 → S
- 1,407 → A
- 550 → R
- 874 → E
- 1,170 → 78×15 → B
- 400 → 25×16 → L
- 1,534 → 59×26 → U
- 874 → E

So second row:

First group: 1,420 → M; 1,407 → A; 550 → R; 495 → S → M A R S

Second group: 1,407 → A; 550 → R; 874 → E → A R E

Third group: 1,170 → B; 400 → L; 1,534 → U; 874 → E → B L U E

Now putting it all together:

First row: S U N S E T O N

Second row: M A R S A R E B L U E

Wait — that seems off.

But let’s re-express:

Top row:
S U N S E T O N

Then:

- MARS → M A R S
- ARE → A R E
- BLUE → B L U E

But how are they grouped?

Look back:

There are three separate groups in the second row:

- [ ] [ ] [ ] [ ] → 1,420 1,407 550 495 → M A R S
- [ ] [ ] [ ] → 1,407 550 874 → A R E
- [ ] [ ] [ ] [ ] → 1,170 400 1,534 874 → B L U E

So the full message is:

SUNSET ON MARS ARE BLUE

Wait — that doesn't make sense.

But “MARS” is a planet, and “blue” is not typical.

Wait — perhaps it's “MARS IS BLUE” or something else.

But we have “ARE”.

Wait — let’s double-check the assignments.

Wait — we have:

- 1,407 → A (from 67×21)
- 550 → R (22×25)
- 874 → E (46×19)

So “A R E” → “ARE”

And “B L U E” → from:

- 1,170 → B (78×15)
- 400 → L (25×16)
- 1,534 → U (59×26)
- 874 → E (46×19)

Yes.

So the message is:

SUNSET ON MARS ARE BLUE

But that’s grammatically odd.

Wait — perhaps it’s “SUNSET ON MARS IS BLUE” — but we don’t have an “I” or “S” for “IS”.

Wait — we have “ARE”, not “IS”.

But maybe it’s a fun fact about Mars?

Wait — let’s reconsider.

Wait — what if the first row is “SUNSET ON”, and second row is “MARS ARE BLUE”?

But “Mars are blue”? That’s not true.

But wait — actually, Mars is red, so perhaps the fun fact is “Sunset on Mars is blue”?

Ah! That’s a real fun fact!

Even though Mars is red, sunsets on Mars appear blue due to the way dust scatters light.

So the message is:

> SUNSET ON MARS ARE BLUE

But “are” is plural — should be “is”.

Wait — unless it’s a typo.

Wait — maybe it's “SUNSET ON MARS IS BLUE” — but we don’t have “I” or “S” for “IS”.

But we do have “S” from 495 → S, and “I” is not in our letters.

We have:

Letters used: A, B, E, L, M, N, O, R, S, T, U

No “I” — so “IS” isn’t possible.

But “ARE” is there.

Wait — could it be “SUNSET ON MARS ARE BLUE” — but that’s awkward.

Wait — perhaps it’s “SUNSET ON MARS IS BLUE” — but we don’t have “I”.

Unless... maybe we misread.

Wait — let’s check the first row again.

First row:

Boxes: [ ] [ ] N [ ] [ ] [ ] [ ] [ ] N

Numbers: 495 1,534 1,650 495 874 900 495 830 1,650

We said:

- 495 → S
- 1,534 → U
- 1,650 → N
- 495 → S
- 874 → E
- 900 → T
- 495 → S
- 830 → O
- 1,650 → N

So: S U N S E T O N

But “SUNSET ON” — yes.

But “SUNSET ON” is 8 letters: S-U-N-S-E-T-O-N → that’s 8 letters.

Wait — “SUNSET ON” is 8 characters: S-U-N-S-E-T- -O-N → but we have 9 boxes.

Wait — the first row has:

- 7 boxes: [ ][ ][N][ ][ ][ ][ ] → 7 boxes
- Then a space
- Then [ ][N] → 2 boxes

Total: 9 boxes.

Our assignment:

1. 495 → S
2. 1,534 → U
3. 1,650 → N
4. 495 → S
5. 874 → E
6. 900 → T
7. 495 → S
8. 830 → O
9. 1,650 → N

So: S U N S E T S O N

Wait — that’s “SUNSETS ON”?

But “SUNSETS” is plural — but we only have one sunset.

Wait — but “SUNSET ON” is 8 letters — but we have 9 positions.

Wait — let’s count:

- Box 1: 495 → S
- Box 2: 1,534 → U
- Box 3: 1,650 → N
- Box 4: 495 → S
- Box 5: 874 → E
- Box 6: 900 → T
- Box 7: 495 → S
- Box 8: 830 → O
- Box 9: 1,650 → N

So: S U N S E T S O N

Wait — that’s “SUNSETS ON”?

But “SUNSETS” is 8 letters — but we have “S-U-N-S-E-T-S-O-N” → 9 letters.

Wait — no: “SUNSETS” is S-U-N-S-E-T-S → 7 letters.

But here: positions:

1. S
2. U
3. N
4. S
5. E
6. T
7. S
8. O
9. N

So: SUNSETS ON

But “SUNSETS ON” — not meaningful.

Wait — maybe it’s “SUNSET ON” and the extra S is a mistake?

Wait — perhaps I made a mistake.

Wait — the third box is N, and the number is 1,650, which is correct.

But the fourth box is 495 → S

Fifth: 874 → E

Sixth: 900 → T

Seventh: 495 → S

So far: S U N S E T S

Then eighth: 830 → O

Ninth: 1,650 → N

So: S U N S E T S O N

But “SUNSETS ON” — still odd.

Wait — perhaps it’s “SUNSET ON MARS ARE BLUE” — but “SUNSET ON” is 8 letters, but we have 9.

Wait — let’s look at the second row.

Second row:

Group 1: 1,420 → M; 1,407 → A; 550 → R; 495 → S → MARS

Group 2: 1,407 → A; 550 → R; 874 → E → ARE

Group 3: 1,170 → B; 400 → L; 1,534 → U; 874 → E → BLUE

So second row: MARS ARE BLUE

Now first row: SUNSET ON

But “SUNSET ON” — but we have 9 boxes.

Wait — perhaps the first row is:

[ S ] [ U ] [ N ] [ S ] [ E ] [ T ] [ O ] [ N ] ? No — we have 9 boxes.

Wait — the layout is:

First row: 7 boxes, then two more.

But the numbers are:

495, 1,534, 1,650, 495, 874, 900, 495, 830, 1,650

That’s 9 numbers.

So 9 boxes.

We have:

1. 495 → S
2. 1,534 → U
3. 1,650 → N
4. 495 → S
5. 874 → E
6. 900 → T
7. 495 → S
8. 830 → O
9. 1,650 → N

So: S U N S E T S O N

But that’s “SUNSETS ON” — but “SUNSETS” is plural.

But “SUNSET ON MARS ARE BLUE” — maybe it’s a typo.

But the real fun fact is:

> Sunsets on Mars are blue — because the dust particles scatter blue light.

So the message should be: SUNSET ON MARS ARE BLUE

But we have “SUNSETS ON” — which is wrong.

Wait — perhaps the first row is not “SUNSETS ON”, but something else.

Wait — let’s check the number 495 — appears multiple times.

495 → S (from 45×11)

Is there another product that gives 495?

No — only 45×11 = 495.

So S is only for 495.

Similarly, 1,650 → N (only from 50×33)

830 → O (83×10)

900 → T (30×30)

874 → E (46×19)

So all are unique.

So the first row must be: S U N S E T S O N

But that’s “SUNSETS ON” — which doesn’t make sense.

Wait — unless it’s “SUNSET ON” and the extra S is a mistake?

But no — we have 9 boxes.

Wait — perhaps the first box is not 495?

Let’s look at the image description.

It says:

```
[ ] [ ] N [ ] [ ] [ ] [ ] [ ] N
495 1,534 1,650 495 874 900 495 830 1,650
```

So:

- Box 1: 495 → S
- Box 2: 1,534 → U
- Box 3: 1,650 → N (given)
- Box 4: 495 → S
- Box 5: 874 → E
- Box 6: 900 → T
- Box 7: 495 → S
- Box 8: 830 → O
- Box 9: 1,650 → N

So: S U N S E T S O N

But “SUNSETS ON” — but “SUNSETS” is not a word.

Wait — perhaps it’s “SUNSET ON” and the extra S is for “S” in “SUNSET”?

No — “SUNSET” is S-U-N-S-E-T → 6 letters.

But we have 9 letters.

Wait — perhaps the message is:

SUNSET ON MARS ARE BLUE

But how to fit?

Let’s try to see if we can reorder.

Wait — maybe the first row is “SUNSET ON”, and the second row is “MARS ARE BLUE”, but the first row has 9 boxes.

Wait — perhaps the first row is “SUNSET ON” (8 letters), but we have 9 boxes.

Unless the “N” in the third box is part of “ON”.

But “ON” is O and N.

We have:

- Box 8: 830 → O
- Box 9: 1,650 → N

So “ON” is at the end.

So “SUNSET ON” would require:

- S, U, N, S, E, T, O, N → 8 letters

But we have 9 boxes.

Wait — unless the first box is not part of the message.

Wait — no — the instruction says: “Put the letter in every box that it matches your answer.”

So we must fill all boxes.

Perhaps the message is:

SUNSET ON MARS ARE BLUE

But that’s 18 letters.

We have:

- First row: 9 boxes
- Second row: 4+3+4 = 11 boxes → total 20 boxes

Too many.

Wait — let’s count:

First row: 7 + 2 = 9 boxes

Second row: 4 + 3 + 4 = 11 boxes

Total: 20 boxes

But the message is likely short.

Wait — perhaps the message is:

SUNSET ON MARS ARE BLUE

But let’s see the numbers:

In the second row:

- MARS: 1,420 (M), 1,407 (A), 550 (R), 495 (S) → MARS
- ARE: 1,407 (A), 550 (R), 874 (E) → ARE
- BLUE: 1,170 (B), 400 (L), 1,534 (U), 874 (E) → BLUE

So: MARS ARE BLUE

Now first row: S U N S E T S O N

But “SUNSETS ON” — but perhaps it’s a typo, and it’s meant to be “SUNSET ON” with the extra S being a mistake.

Wait — perhaps the number 495 appears three times, but only one S.

But we have to put S in every box that matches.

So if a number appears multiple times, we put the same letter in all.

So for 495 → S, and it appears 3 times in first row, so three S’s.

Similarly, 1,650 appears twice → two N’s.

So the first row is: S U N S E T S O N

But “SUNSETS ON” — but “SUNSETS” is not standard.

Wait — perhaps it’s “SUNSET ON” and the extra S is for “S” in “SUNSET”, but we already have it.

Wait — let’s write the whole thing:

From first row: S U N S E T S O N

From second row: M A R S A R E B L U E

But “SUNSETS ON MARS ARE BLUE” — that’s grammatically incorrect.

But perhaps it’s “SUNSET ON MARS ARE BLUE” — but we have “SUNSETS”.

Unless the intended message is “SUNSET ON MARS IS BLUE” — but we don’t have “I”.

Wait — unless “ARE” is a typo for “IS”, but we have “ARE”.

But “ARE” is from 1,407 (A), 550 (R), 874 (E) — so it’s correct.

But perhaps the fun fact is: “Sunsets on Mars are blue” — even if it’s plural.

But “sunsets” is plural.

And “are” is plural.

So: Sunsets on Mars are blue — makes sense.

But we have “SUNSETS ON” — but “SUNSETS” is not in the first row.

Wait — we have:

- S, U, N, S, E, T, S, O, N → “SUNSETS ON”

But “SUNSETS” is S-U-N-S-E-T-S — 7 letters, but we have S-U-N-S-E-T-S-O-N — 9 letters.

Wait — “SUNSETS ON” — but “SUNSETS” is 7 letters, “ON” is 2, total 9.

Yes.

So the message is: SUNSETS ON MARS ARE BLUE

But that’s “Sunsets on Mars are blue” — which is correct.

And it’s a fun fact.

So the complete message is:

SUNSETS ON MARS ARE BLUE

But why “SUNSETS” instead of “SUNSET”?

Because the word “SUNSET” has an 'S' at the beginning and end, and we have multiple 495s, so multiple S’s.

So it's acceptable.

Thus, the final message is:

> SUNSETS ON MARS ARE BLUE

Which is a fun fact: Sunsets on Mars are blue due to atmospheric scattering.

---

Final Answer:

The completed message is:

SUNSETS ON MARS ARE BLUE

With the following:

- First row: S U N S E T S O N
- Second row: M A R S A R E B L U E

And the fun fact is: Sunsets on Mars are blue — even though Mars is red, the thin atmosphere causes blue sunsets.

✔ Solution Complete