Math Riddles with Answers

There were only three people. A grandfather, his son, and his grandson make two fathers and two sons.

Grandfather, father, and son are three people who count as two fathers and two sons, so three fish match three anglers.

Zero. Any number times zero is always zero.

Any number times zero equals zero, so the product never changes.

1, 2 and 3. Both the sum and the product equal 6.

1 plus 2 plus 3 is 6 and 1 times 2 times 3 is also 6.

9. The phrase all but 9 means exactly 9 stayed behind.

All but 9 ran away means exactly 9 stayed, so 9 remain.

3. You took them, so those are the ones you have.

You physically remove 3 apples, so the 3 you took are the ones you have.

33. Each number is double the previous one minus 1.

The gaps 1, 2, 4, 8 double each step, so add 16 to 17 to get 33, matching double minus one.

Only one. After the first egg the basket is no longer empty.

The width is a distractor; once the first egg is inside the basket is no longer empty, so the count is one.

3. Three ducks in a single row satisfy all three descriptions at the same time.

Three ducks in a line: two lead the last one, two trail the first one, and the middle one is between them.

Four. The word four is spelled with exactly four letters.

The word f-o-u-r has four letters, matching its value of four.

On a clock. Two hours after 11 o'clock it is 1 o'clock.

On a 12 hour clock, adding 2 hours to 11 wraps past 12 and lands on 1.

36. These are the square numbers, and 6 times 6 is 36.

The terms are the squares 1,4,9,16,25, so the next is 6 squared, which is 36.

1. Halving 8 three times gives 4, then 2, then 1.

8 times one half cubed equals 8, 4, 2, 1.

Neither side. Roosters do not lay eggs.

A rooster is male and lays no egg, so nothing rolls down either side.

5050. Pair 1 with 100, 2 with 99, and so on: fifty pairs that each add up to 101.

Pair 1+100, 2+99, and so on: fifty pairs of 101 give 5050.

48. Each number is double the one before it.

Each term doubles the previous, so 24 times 2 is 48.

6. Four times 6 is 24, minus 6 is 18, and 18 is three times 6.

Set 4x minus 6 equals 3x, so x is 6, and 24 minus 6 is 18 which is 3 times 6.

1 and 31. It is a prime number, so no other pair of whole numbers works.

31 is prime, so only 1 times 31 gives 31.

None. A hole is empty, that is what makes it a hole.

A hole is defined by absence of dirt, so it contains none regardless of its size.

Zero. The keypad includes a 0, and anything multiplied by zero is zero.

The keypad includes a 0 key, and any product times zero equals zero.

8. Both recipes give 36, since 3 times 8 plus 12 equals 5 times 8 minus 4.

Set 3x+12=5x-4, so 16=2x and x=8, and both sides equal 36.

Two kilograms. If half a brick weighs one kilogram, the whole brick weighs two.

Write b=1+b/2, so b/2=1 and b=2 kilograms.

Day 47. One more doubling turns half a lake into a full lake.

Since it doubles daily and is full on day 48, the previous day 47 shows half.

5 minutes. Each machine makes one widget in 5 minutes, no matter how many machines run at once.

5 machines make 5 widgets in 5 minutes means each machine makes one widget in 5 minutes, so 100 machines make 100 widgets in 5 minutes.

Day 9. The ninth cut splits the final 6 meters into two pieces, so there is nothing left to cut on day 10.

Ten 3 meter pieces need only nine cuts, and the ninth cut splits the last 6 meters into two, so day 9 is the last cut.

70. Dividing by a half doubles a number, so 30 becomes 60, plus 10 is 70.

Dividing by one half is the same as multiplying by 2, so 30 becomes 60, then plus 10 gives 70.

One thousand. Every number from 1 to 999 avoids the letter a completely.

Every number name from one through nine hundred ninety-nine avoids a, and thousand (t-h-o-u-s-a-n-d) is the first to include it.

Six dozen dozen. That works out to 864, while half a dozen dozen is only 72.

Six dozen dozen is 6 times 12 times 12 equals 864, and half a dozen dozen is 6 times 12 equals 72, so 864 is bigger.

Two. Each quarter travels with two dimes, and two of those 45 cent bundles make 90 cents.

With q quarters and 2q dimes, 25q plus 10 times 2q equals 45q equals 90, so q equals 2.

8 days. It gains 1 meter per full day, and on day 8 it climbs from 7 meters to the top before the night slip.

Each morning the snail sits at n minus 1 meters and climbs to n plus 2, which first reaches 10 when n is 8.

Write nine as the Roman numeral IX and cut it in half horizontally. The top half reads IV, which is four.

Nine is the Roman numeral IX, and a horizontal cut leaves IV on top, which is four.

10. The father is 40, and in 20 years they will be 60 and 30, which fits both facts.

Let the son be s and father 4s: 4s plus 20 equals 2 times (s plus 20), so 2s equals 20 and s equals 10.

18 dollars. The shop charges 4.50 per leg, and a cat has four legs.

Each animal costs 4.50 per leg: duck 2 legs is 9, spider 8 is 36, bee 6 is 27, so a cat with 4 legs is 18.

54. One hen lays two thirds of an egg per day, so 9 hens times 9 days times two thirds gives 54.

1.5 hens lay 1.5 eggs in 1.5 days, so 1 hen lays 1 egg in 1.5 days, which is two thirds of an egg per day; 9 times 9 times two thirds is 54.

888 + 88 + 8 + 8 + 8. Those five numbers use eight 8s and add up to exactly 1000.

888 plus 88 is 976, and 8 plus 8 plus 8 is 24, giving 1000 while using three plus two plus three, which is eight 8s.

Still 3. Each cat catches one mouse every 3 minutes, so 3 cats catch about 100 mice in 100 minutes.

Three cats catch three mice in three minutes means one cat catches one mouse every three minutes, so the same 3 cats catch 100 mice in 100 minutes.

36. Reversed it becomes 63, which is 27 more, and 3 plus 6 equals 9.

Reversing 10a plus b changes it by 9 times (b minus a) equals 27, so b minus a is 3; with a plus b equals 9 that gives a equals 3, b equals 6, so 36.

4100. Most people blurt out 5000 because the small additions feel like they build another thousand.

The four thousands sum to 4000, and 40+30+20+10 is 100, so the total is 4100 not 5000.

10 dollars. Work backwards: 10 plus 10 is 20, halve it to 10, add 10 to get 20, halve it to 10.

Let x be the start: 2(2x-10)-10=10 gives 4x-30=10, so 4x=40 and x=10.

63. Every match eliminates exactly one player, and 63 players must go home before a champion remains.

Each match eliminates one player, and 64 players need 63 eliminated to leave one champion.

12. In two years I will be 14, which is double the 7 I was five years ago.

Solve x+2=2(x-5): x+2=2x-10 gives x=12, and 14 is twice the 7 of five years ago.

5 cents. Then the bat costs 1.05, which is exactly one dollar more.

Ball plus ball plus 1 equals 1.10, so 2 times ball is 0.10 and ball is 0.05.

312211. Each term reads the previous one out loud, so three 1s, two 2s, one 1.

This is look and say, so 111221 reads as three 1s, two 2s, one 1, giving 312211.

There is no missing dollar. The 27 they paid already includes the bellboy's 2, so adding it again counts it twice.

The 27 paid is 25 kept by the room plus 2 kept by the bellboy, and adding the 3 refunded gives 30, so nothing is missing.

86. Turned upside down it reads 98, which is exactly 12 more.

Only 0,1,6,8,9 stay readable flipped; checking valid two-digit cases, 86 flips to 98 and 98 minus 86 equals 12, the smallest such number.

50 kg. The 1 kg of dry matter must now make up 2 percent of the whole, so the whole is 50 kg.

Dry matter is 1 percent of 100 kg equals 1 kg and stays fixed; at 98 percent water it is 2 percent, so total is 1 divided by 0.02 equals 50 kg.

1961. Flip the digits and they still read 1961.

Only 0,1,8 stay and 6,9 swap; rotating 1961 by 180 degrees gives 1961, and no strobogrammatic year exists between 1962 and 2026.

5 cows, 1 pig and 94 chickens. That is exactly 100 animals for exactly 100 dollars.

5 cows cost 50, 1 pig costs 3, 94 chickens cost 47: 50+3+47 is 100 dollars and 5+1+94 is 100 animals.

Its digits appear in alphabetical order: eight, five, four, nine, one, seven, six, three, two, zero.

Spelling the digits gives eight, five, four, nine, one, seven, six, three, two, zero, which is alphabetical order.

5/8. Eating 3 of the 8 slices leaves 5 slices.

Eight slices minus the three eaten leaves five out of eight, so 5/8 remains.

25. The pattern counts up by fives.

Each term adds 5, so after 20 comes 25.

Wednesday. Seven days is one full week, so the day repeats.

A week is exactly seven days, so the same weekday returns.

7. A triangle has 3 sides and a square has 4.

Three sides plus four sides gives seven.

2. Every other even number can be divided by 2, so it is not prime.

2 is divisible only by 1 and itself, and all larger even numbers have 2 as a factor.

60. Each step subtracts 10.

The pattern counts down by ten, so after 70 comes 60.

26. Two times 13 is 26.

Doubling a baker's dozen of 13 gives 26.

25 dollars. The sale price of 20 is 80 percent of the original.

Since 20 dollars is 80 percent of the original, dividing 20 by 0.8 gives 25.

12. Jerry is 9 and Tom is 3 years older.

Removing the 3 year gap leaves 18 to split evenly, so Jerry is 9 and Tom is 12.

165 minutes. That is 2 hours and 45 minutes.

From 2:15 to 5:00 is 2 hours and 45 minutes, which is 120 plus 45 equals 165 minutes.

2 dollars. Three pens cost 9, leaving 4 dollars for two pencils.

Three pens use 9 dollars, so the two pencils share the remaining 4, which is 2 each.

20. Each orange costs 50 cents.

Four oranges for 2 dollars means 50 cents each, so 10 dollars buys 20.

Fill the 5, pour into the 3 to leave 2, empty the 3, move the 2 over, refill the 5, then top off the 3 which takes 1, leaving 4 in the big jug.

Pouring between the jugs isolates exactly 4 liters in the 5 liter jug.

21. Ten times in the units place, ten in the tens place, and once in 100.

The units digit is 1 ten times, the tens digit is 1 ten times, and 100 adds one more, giving 21.

99. Pages 1 to 9 use 9 digits and pages 10 to 99 use 180 more.

The single digit pages use 9 digits and the ninety two digit pages use 180, totaling 189 for 99 pages.

90 miles. The trains meet in one hour, so the bird flies for one hour.

The trains close at 100 mph and meet in 1 hour, so the 90 mph bird covers 90 miles.

Yes. The chance passes 50 percent at 23 people.

There are many possible pairs, so the odds of a shared birthday just cross one half at 23 people.

1. The last digits of powers of 7 cycle 7, 9, 3, 1.

Powers of 7 end in a repeating block of 7, 9, 3, 1, and 100 is a multiple of 4 so it lands on 1.

The chicken. That leaves the fox and grain safely together.

Moving the chicken first prevents both dangerous pairings on either bank.

One half. Each flip is independent of the ones before.

A fair coin has no memory, so the odds stay even no matter the streak.

Turn one on a while then off, turn a second on, and go up: lit is the second, warm and dark is the first, cold and dark is the third.

Using both light and leftover heat gives two clues, enough to identify all three in a single trip.

Still 4. The boat floats up with the water, lifting the ladder too.

Because the boat rises with the tide, the waterline stays at the same rung.

204. It adds the square numbers 1, 4, 9, and so on up to 64.

Counting squares of each size gives 1 plus 4 plus 9 and so on to 64, which totals 204.

6 minutes. The eggs boil at the same time.

All three eggs cook simultaneously in the same water, so the time does not increase.

40 meters. Down 16, up 8, down 8, up 4, down 4.

Summing 16 down, then 8 up and 8 down, then 4 up and 4 down gives 40 meters at the third landing.

57. Fifty four with single digit hours plus three more at 10, 11, and 12.

Single digit hours give 9 times 6 palindromes and the hours 10, 11, and 12 give one each, totaling 57.

2. Split the coins into three groups of three.

One weighing of two groups of three finds the light group, and a second weighing within it finds the coin.

10. Ten people make 45 different pairs.

The number of handshakes is n times n minus 1 over 2, which equals 45 when n is 10.

2 hours and 24 minutes. That is twelve fifths of an hour.

Setting the slow candle's remaining length to twice the fast one's and solving gives 12/5 hours, or 2 hours 24 minutes.

40 mph. Average speed is total distance over total time, not the average of the two speeds.

The slower leg takes more time, so weighting by time gives 40 mph rather than 45.