ARITHMETIC EXAM

A lump of cheese can be chopped into a maximum of 93 pieces with eight straight cuts.

The number four is the only number in the English language that is spelled with the same number of letters as the number itself.

Forty is the only number with all its letters in alphabetical order, and one is the only number to have its letters in reverse alphabetical order.

Twenty-nine is the only number that is written with as many strokes as its numerical value (if Y is written with three strokes).

An “octillion” is the lowest positive number to contain a letter C.

The number 172 can be found on the back of the five-dollar bill in the bushes at the base of the Lincoln Memorial.

A mile on land is 5,280 feet. A nautical mile is 6,080 feet.

A carat, the measurement of gems, is 200 milligrams, nearly the equivalent the weight of the carab seed on which it was based.

A pound of gold actually weighs less than a pound of feathers. The reason is that feathers are measured in avoirdupois weight in which there are 16 ounces per pound. Gold is measured in troy weight with 12 ounces per pound.

If 1089 is multiplied by 9, the result is the number’s reverse, 9801. This also works with 10989 or 109989 or 1099989 and so on.

1 is the only positive whole number that can be added to 1,000,000 and will result in an answer that’s bigger than if it is multiplied by 1,000,000.

19 = 1 × 9 + 1 + 9 and 29 = 2 × 9 + 2 + 9. This also works for 39, 49, 59, 69, 79, 89, and 99.

153, 370, 371, and 407 are all the “sum of the cubes of their digits.” In other words, 15³ = 1³ + 5³ + 3³.

Any square number divided by 8 results in a remainder of 0, 1, or 4.

2 is the only number that gives the same result added to itself as it does multiplied by itself.

There are 12,988,816 different ways to cover a chessboard with 32 dominoes.

69 squared = 69² = 4761, and 69 cubed = 69³ = 328509. These two answers use all the digits from 0 to 9 between them. As does 18³ = 5832, and 18⁴ = 104976.

1 divided by 37 equals 0.027027027 . . . and 1 divided by 27 equals 0.037037037.

13² = 169, and if both numbers are written backward the result is 31² = 961. This also works with 12 because 12² = 144, and 21² = 441.

8 is the only cube that is 1 less than a square.

To multiply 10,112,359,550,561,797,752,808,988,764, 044,943,820,224,719 by 9, move the 9 at the very end up to the front. This is the only equation that can be solved in such a way.

1 × 9 + 2 = 11, 12 × 9 + 3 = 111, 123 × 9 + 4 = 1111, and so on.

There are 169,518,829,100,544,000,000,000,000,000 ways to play the first ten moves in a game of chess.

3,608,528,850,368,400,786,036,725 contains 25 digits and divides evenly by 25.

The biggest number that can be made with three digits and any operators is 9 to the power of 9 to the power of 9. As 9⁹ = 387,420,489, the final number is 9,387,420,489 = about 200 million digits.

To add all the numbers from 1 to 10, divide the 10 by 2, then write the answer out twice—it equals 55. This also works when adding the numbers from 1 to 100, 1 to 1,000, and so on.

144 is the 12th number in the Fibonacci series 144 and is also the result of 12².

1,274,953,680 uses all the digits from 0 to 9 and can be divided exactly by any number from 1 to 16.

There is something curious in the properties of the number 9. Any number multiplied by 9 produces a sum of figures that, added together, continually makes 9. For example, all the first multiples of 9—18, 27, 36, 45, 54, 63, 72, 81—add up to 9. Each of them multiplied by any number produces a similar result: 8 × 8 1 = 648; these added together make 18: 1 and 8 = 9; multiply 648 by itself, the product is 419,904—the sum of these digits is 27: 2 + 7 = 9.

What 5-digit number, when multiplied by the number 4, is the same number with the digits in reverse order? 21978; 21978 × 4 = 87912.

111,111,111 × 111,111,111 = 12,345,678,987,654,321