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NUMBERS

• If you multiply 1,089 by 9, you get 9,801. It’s reversed itself! This also works with 10,989 or 109,989 or 1,099,989 and so on.

• 1 is the only positive whole number you can add to 1,000,000 and get an answer that’s bigger than if you multiply it by 1,000,000.

• 19 = 1 x 9 + 1 + 9 and 29 = 2 x 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 = 1 + 125 + 27.

• If you divide any square number by 8, you get a remainder of 0, 1 or 4.

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

• If you multiply 21,978 by 4, it turns backwards.

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

• 69 squared = 69² = 4,761 and 69 cubed = 69³ = 328,509. These two answers use all the digits from 0 to 9 between them. As does 18³ = 5,832 and 184 to the power of 4 = 104,976.

• You can chop a big lump of cheese into a maximum of ninety-three bits with eight straight cuts.

• In the English language, ‘forty’ is the only number that has all its letters in alphabetical order.

• 1 ÷ 37 = 0.027027027… and 1 ÷ 27 = 0.037037037…

• 13² = 169 and if you write both numbers backwards you get 31² = 961. This also works with 12, because 12² = 144 and 21² = 441.

• 1/1089 = 0.00091827364554637281… (And the numbers in the 9 times table are 9, 18, 27, 36…)

• 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 you just move the 9 at the very end up to the front. It’s the only number that does this.

• The number 4 is the only number in the English language that is spelled with the same number of letters as the number itself.

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

• Twenty-nine is the only number that is written with as many strokes as its numerical value! (You need to write ‘Y’ with three strokes.)

• 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 has twenty-five digits and divides by 25.

• An ‘octillion’ is the lowest positive number to contain a letter ‘c’.

• One is the only number in the English language to have its letters in reverse alphabetical order.

• The biggest number you can make with three digits and any operators is 9 to the power of 9 to the power of 9. As 9 to the power of 9 = 387, 420, 489, the final number is 9^{387, 420, 489} = a number that is over 200 million digits!

• 1 ÷ 14 = 0.0714285714285714285… and 7, 14 and 28 are factors and multiples of 14 and the 5 tells you how many digits 71428 has before they repeat!

• To add all the numbers 1–10, you just divide the 10 by 2 then write the answer out twice = 55. Also all the numbers 1–100 are 100 divided by 2 written twice, i.e. 5,050. This also works for 1–1,000, 1–10,000, 1–100,000, etc!

• 144 is the twelfth number in the Fibonacci series. 144 is also 12².

• All the numbers from 12 to 242 added together equal 70².

• 1,274,953,680 uses all the digits 0–9 and you can divide it 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 x 81 = 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. The rule is invariable.

• A mile on land is 5,280ft (1,609m) long. A nautical mile is 6,080ft (1,853m).

• A carat, the measurement of gems, is 200mg, nearly the equivalent of a carb seed on which it was based.

• A pound of gold actually weighs less than a pound of feathers. Explanation: feathers are measured in avoirdupois weight, in which there are 16 oz per pound. Gold is measured in troy weight, with 12oz per pound.

• If you add up the numbers 1–100 consecutively (1 + 2 + 3 + 4 + 5, etc), the total is 5,050.

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

• 111,111,111 x 111,111,111 = 12,345,678,987,654,321.