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Fun Arithmetic Created by Inna Shapiro ©2008

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Problem 1 Max has ten cards with the digits 0, 1, 2,…9. He can arrange these cards into different 10-digit numbers. What is the greatest number that he can get?

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Answer The greatest number should start with the greatest digit 9. The second digit will be the greatest of the rest, i.e. 8, and so on. The greatest number is 9876543210.

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Problem 2 A teacher has four cards with numbers. The sum of these numbers is equal to 8. When the teacher shows these cards to Mary and asks to multiply the numbers, Mary also gets 8. What numbers are on the cards? Some numbers could be equal.

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Answer The numbers are 1, 1, 2, and 4.

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Problem 3 Ron has five cards with the digit 1. How can he arrange them to compose the number 100 using the arithmetic operations +, -, *, and / ?

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Answer 100=111-11

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Problem 4 Monty has five cards with the digit 5. How can he arrange his cards to get the number 100 using the arithmetic operations +, -, *, and / ?

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Answers 100=5*5*5-5*5 100=(5+5+5+5)*5

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Problem 5 There are nine cards with different digits 1,2,3,4,5,6,7,8,9. Can you compose number 100 using all these cards in the same order and the arithmetic operations +, -, *, and / ?

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Answers 100=1+2+3+4+5+6+7+8*9 100=1*23+4+5+67-8+9

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Problem 6 Can you replace # by arithmetic operations so that the following expression will be equal to 100? You can use parentheses. 1#2#3#4#5

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Answer 100=1*(2+3)*4*5

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Problem 7 Jerry has four cards with the digit 2. How can he arrange these cards to get 0, 1, 2, 3, 4, 5, 6, 8, 9, or 10? Jerry can use arithmetic operations +, -, *, and /.

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Answer 22-22=0 22:22=1 2:2+2:2=2 (2+2+2):2=3 2*2+2-2=4

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Answer /continued/ 2*2+2:2=5 2*2*2-2=6 2 +2+2+2=8 22:2-2=9 2*2*2+2=10

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Problem 8 Can you put in parentheses so that this expression will be equal to 23? 7*9+12:3-2

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Answer 23=(7*9+12):3-2

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Problem 9 Can you put parentheses in the same expression to make it equal to 75? 7*9+12:3-2

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Answer 75=(7*9+12):(3-2)

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Problem 10 Put numbers into this table so that the sum of any three adjacent cells equals 15. 64

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Answer The number in each cell must be the same as the number in any cell three slots away from it. Lets fill the table step by step. 666466 646464646 6546546546546

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