Math Should Never Be Boring! More Math Brain-Teasers (Free ... - Free Printable

Let’s go through each riddle one by one, solve them carefully, and then give the final answers.

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Riddle 1: Barrel of water — measure 1 gallon with a 3-gallon and 5-gallon container

We need to get exactly 1 gallon using only these two containers.

Step-by-step:

- Fill the 5-gallon container.
- Pour from the 5-gallon into the 3-gallon until it’s full → now 5-gallon has 2 gallons left.
- Empty the 3-gallon container.
- Pour the 2 gallons from the 5-gallon into the 3-gallon container.
- Fill the 5-gallon container again.
- Pour from the 5-gallon into the 3-gallon (which already has 2 gallons) → you can only pour 1 more gallon to fill it.
- Now the 5-gallon container has 4 gallons? Wait — no! Let’s correct:

Actually, after pouring 1 gallon into the 3-gallon (to top it up), the 5-gallon container will have 4 gallons? That doesn’t help us get 1.

Wait — let’s try again:

Better way:

- Fill the 3-gallon container.
- Pour it into the 5-gallon container.
- Fill the 3-gallon again.
- Pour into the 5-gallon until it’s full → that takes 2 gallons, so 1 gallon remains in the 3-gallon container.

✔ Yes! So we have 1 gallon left in the 3-gallon container.

Answer for #1: Fill the 3-gallon, pour into 5-gallon. Fill 3-gallon again, pour into 5-gallon until full — 1 gallon remains in the 3-gallon container.

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Riddle 2: Socks — minimum to guarantee a matching pair

You have:
- 6 black
- 4 blue
- 8 brown
- 2 red

Total colors = 4

Worst case: You pick one sock of each color first → 4 socks, all different.

The next sock (5th) must match one of them.

So, minimum to be sure = 5 socks

Answer for #2: 5

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Riddle 3: Easiest way to double your money

This is a joke/riddle.

Answer: Put it in front of a mirror! 😄

Or sometimes: “Double it” — but the classic answer is the mirror trick.

Answer for #3: Put it in front of a mirror

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Riddle 4: Which month has 28 days?

All months have at least 28 days. February has exactly 28 (or 29), but every month has *at least* 28.

So the trick question answer is: All of them

Answer for #4: All months

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Riddle 5: Merchant shipping boxes

He can put:
- 8 large boxes per carton OR
- 10 small boxes per carton

Total boxes shipped: 96

More large boxes than small boxes.

Let L = number of cartons with large boxes
S = number of cartons with small boxes

Then:
8L + 10S = 96
And: 8L > 10S (more large boxes than small)

Also, L and S are non-negative integers.

Try possible values:

Start with S=0 → 8L=96 → L=12 → 8*12=96, 10*0=0 → 96>0 → OK, but does he ship any small boxes? The problem says “he sent a total of 96 boxes”, and “more large than small” — if S=0, then small=0, so technically more large than small? But maybe they mean both types were shipped? Let’s check other options.

Try S=1 → 10*1=10 → 8L=86 → not divisible by 8 → no

S=2 → 20 → 8L=76 → no

S=3 → 30 → 8L=66 → no

S=4 → 40 → 8L=56 → L=7 → 8*7=56, 10*4=40 → 56>40 → YES!

Check total: 56+40=96 ✔

Cartons: L+S = 7+4 = 11

Is there another solution?

S=5 → 50 → 8L=46 → no

S=6 → 60 → 8L=36 → no

S=7 → 70 → 8L=26 → no

S=8 → 80 → 8L=16 → L=2 → 16 vs 80 → 16 < 80 → violates “more large than small”

S=9 → 90 → 8L=6 → no

S=10 → 100 > 96 → too big

Only valid solution with more large than small is L=7, S=4 → total cartons = 11

Answer for #5: 11

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Riddle 6: Frog in hole

Hole depth: 14½ feet = 14.5 ft

Jumps 3 feet, slides back 1 foot each time → net gain per jump = 2 feet

BUT — on the last jump, when he reaches or exceeds 14.5, he gets out and doesn’t slide back.

So, how many jumps?

After n-1 jumps, he is at 2*(n-1) feet.

On the nth jump, he jumps 3 feet → position = 2(n-1) + 3

Set this ≥ 14.5

2(n-1) + 3 ≥ 14.5
→ 2n - 2 + 3 ≥ 14.5
→ 2n +1 ≥ 14.5
→ 2n ≥ 13.5
→ n ≥ 6.75 → so n=7

Check:

Jump 1: 0 +3 -1 = 2
Jump 2: 2+3-1=4
Jump 3: 6
Jump 4: 8
Jump 5: 10
Jump 6: 12
Jump 7: 12 +3 = 15 → which is >14.5 → he’s out! No slide back.

Yes, 7 jumps.

Answer for #6: 7

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Riddle 7: Boy’s age

Let current ages:

Boy = B
Sister = S
Father = F

Given:

B = 2S (boy twice as old as sister)
B = 0.5F → F = 2B (boy half as old as father → father twice as old)

In 50 years:

Sister’s age = S + 50
Father’s age = F + 50

And: S + 50 = 0.5 * (F + 50)

Substitute F = 2B and B = 2S → so F = 2*(2S) = 4S

Now plug into future equation:

S + 50 = 0.5 * (4S + 50)

Multiply both sides by 2:

2S + 100 = 4S + 50

100 - 50 = 4S - 2S
50 = 2S
→ S = 25

Then B = 2S = 50

Check:

Current: Boy=50, Sister=25, Father=100

In 50 years: Sister=75, Father=150 → 75 is half of 150 → yes.

Answer for #7: 50

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Riddle 8: How is the moon like a dollar?

Classic riddle.

Answer: Because they both have phases! 🌑🌒🌓 etc.

Or sometimes: “They’re both round” — but “phases” is the clever answer.

Answer for #8: They both have phases

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Riddle 9: Happens once in a minute, twice in a week, once in a year

Look at letters.

“Minute” → contains ‘m’, ‘i’, ‘n’, ‘u’, ‘t’, ‘e’ → look for letter that appears once.

“Week” → w,e,e,k → ‘e’ appears twice.

“Year” → y,e,a,r → ‘e’ appears once.

What about ‘e’? In “minute” — once? M-I-N-U-T-E → yes, one ‘e’.

In “week” — two ‘e’s.

In “year” — one ‘e’.

But the riddle says: “once in a minute, twice in a week, once in a year”

That fits ‘e’ perfectly.

Answer for #9: The letter 'e'

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Final Answers Summary:

1) Fill the 3-gallon, pour into 5-gallon. Repeat — second time, only 1 gallon needed to fill 5-gallon, leaving 1 gallon in 3-gallon container.
2) 5
3) Put it in front of a mirror
4) All months
5) 11
6) 7
7) 50
8) They both have phases
9) The letter 'e'

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Final Answer:
1) Fill the 3-gallon container and pour it into the 5-gallon container. Fill the 3-gallon container again and pour into the 5-gallon until full — 1 gallon remains in the 3-gallon container.
2) 5
3) Put it in front of a mirror
4) All months
5) 11
6) 7
7) 50
8) They both have phases
9) The letter 'e'