# 12 Math Riddles Only the Smartest Can Get Right

## You might want to break out a calculator because it takes a genius to solve these tricky math riddles.

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## House numbers

My twin lives at the reverse of my house number. The difference between our house numbers ends in two. What are the lowest possible numbers of our house?

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These math riddles aren’t easy to solve. Do you think you know the answer to this one? The lowest possible numbers for our house are 19 and 91.

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## Egg equation

If a hen and a half lay an egg and a half in a day and a half, how many eggs will half a dozen hens lay in half a dozen days?

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Two dozen. If you increase both the number of hens and the amount of time available four-fold, the number of eggs increases 16 times. 16 x 1.5 = 24.

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## Card question

A small number of cards has been lost from a complete pack. If I deal among four people, three cards remain. If I deal among three people, two remain and if I deal among five people, two cards remain. How many cards are there?

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There are 47 cards.

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## Knight moves

I have a calculator that can display 10 digits. How many different 10-digit numbers can I type using just the 0-9 keys once each, and moving from one keypress to the next using the knight’s move in chess? (In chess, the knight move in an L-shape – one square up and two across, two squares down and one across, two squares up and one across, and other like combinations.)

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You can form the numbers 5034927618 and 5038167294. You can also form their reverses: 8167294305 and 4927618305. Hence four different numbers can be made. The key point is to realize that the number must start or end on the ‘5’ key, followed/preceded by the ‘0’ key, otherwise, there is no way of using all ten keys during the route.

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## Two by two

You know 2 + 2 comes to the same as 2 x 2. Now find a set of three different whole numbers whose sum is equal to their total when multiplied.

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The three different whole numbers whose sum is equal to their total when multiplied are 1, 2 and 3.

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## Apple harvest

Mrs. Jones was very proud of her apple tree. One autumn, after harvesting her apples, she called her three sons together. “Here are 150 apples,” she said. “I want you to take them to the market tomorrow and sell them for me.” She gave Paul 15 apples, Nick 50, and Ben 85. “Your job,” added Mrs. Jones, “is to sell the apples in such a way that each of you brings home the same amount of money.” How do they do it?

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The first buyer purchases 12 dozen apples at \$1 per dozen. Paul sells him one dozen and has three apples left; Nick sells him four-dozen and has two apples left; and Ben sells him seven-dozen and has one apple left. Then a second buyer comes along and buys all their remaining apples for \$3 apiece. The three brothers head home with \$10 each.

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## Seven times

What is the smallest whole number that is equal to seven times the sum of its digits?

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The answer to this math riddle is 21. You probably just guessed to answer this math riddle, which is fine, but you can also work it out algebraically. The two-digit number ab stands for 10a + b since the first digit represents 10s and the second represents units. If 10a + b = 7(a + b), then 10a + b = 7a + 7b, and so 3a = 6b, or, more simply, a = 2b. That is, the second digit must be twice the first. The smallest such number is 21.

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## Lunch money

John noticed that the amount he was paying for his lunch was a rearrangement of the digits of the amount of money he had in his pocket, and that the money he had left over was yet another rearrangement of the same three digits! How much money did John start with?

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John started with \$9.54. The money can be written with just three digits—so it must be between \$1.01 and \$9.99. Trial and error shows that there is only one set of numbers that fit this question: \$9.54 = \$4.59 + \$4.95. If you can solve these math riddles easily, you’ll want to try your hand at what an MIT professor called the “hardest logic puzzle ever.”

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## Animal riddle

In reply to an inquiry about the animals on his farm, the farmer says: “I only ever keep sheep, goats, and horses. In fact, at the moment they are all sheep bar three, all goats bar four, and all horses bar five.” How many does he have of each animal?

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The farmer has 3 sheep, 2 goats, 1 horse. Adding 3, 4, and 5, in this case, gives twice the number of animals, so there must be six animals altogether.

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## Inheritance

Old Granny Adams left half her money to her granddaughter and half that amount to her grandson. She left a sixth to her brother, and the remainder, \$1,000, to the dogs’ home. How much did she leave altogether?

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She left \$12,000. One half plus one quarter plus one-sixth equals eleven-twelfths. So, the remainder, \$1,000, is one-twelfth of the whole, which must have been \$12,000.

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## Brother puzzle

One brother says of his younger brother: “Two years ago, I was three times as old as my brother was. In three years’ time, I will be twice as old as my brother.” How old are they each now?

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The elder is 17, the younger 7. Two years ago, they were 15 and 5 respectively, and in three years’ time, they will be 20 and 10.

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## Upside down numbers

What is the smallest number that increases by 12 when it is flipped and turned upside down?

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