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Arithmetic Puzzles Created by Inna Shapiro ©2008

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Problem 1 Please, replace the # and & symbols with digits # # + # & 1 9 7

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Answer 9 9 + 9 8 1 9 7

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Problem 2 Please, replace the # and & symbols with digits 1 # # # - & & & 1

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Answer 1 0 0 0 - 9 9 9 1

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Problem 3 Please, replace each letter with a digit: aa + bcb = deed, Note that each of those numbers is its own mirror image (left to right is same as right to left).

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Answer We must find digits, so that the sum looks like aa + bcb = deed. Obviously d=1 and b=9 => aa + 9c9 = 1ee1, that means that a=2, 22 + 9c9 = 1ee1 => e=0 and c=7 22 + 979 = 1001

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Problem 4 Please, replace letters with digits B D C E + B D A E A E C B E

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Answer 5 2 4 0 + 5 2 1 0 1 0 4 5 0

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Problem 5 Please, replace letters with digits a 5 2 b - b 2 5 a 8 c d c

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Answer 9 5 2 1 - 1 2 5 9 8 2 6 2

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Problem 6 How can you replace # and & symbols? 1.#### + 1 = 1&&&& 2.1&&&&&& - 1 = ######

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Answers 1.9999 + 1 = 10000 2.1000000 – 1 = 999999

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Problem 7 Can you change letters a and b to digits? b a a a a + a a a a a a a a b a a a a

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Answer 2 9 9 9 9 + 9 9 9 9 9 9 9 9 2 9 9 9 9

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Problem 8 Please, replace letters with digits to get the correct answer 7abcdef : 5 = abcdef7

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Answer 714285 : 5 = 142857

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Problem 9 Max wrote two-digit number. Then he inserted 0 between the two digits. The result is nine times greater than original number. What was the original number?

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Answer The original number is 45, when Max added 0 he got 405, 45 * 9 = 405

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Problem 10 Please add arithmetic signs and parenthesis to get correct answers: 5 5 5 5 = 3 5 5 5 5 = 4 5 5 5 5 = 5 5 5 5 5 = 6 5 5 5 5 = 7

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Answer (5 + 5 + 5) : 5 = 3 (5 * 5 – 5) : 5 = 4 (5 – 5) * 5 + 5 = 5 (5 * 5 + 5) : 5 = 6 (5 + 5) : 5 + 5 = 7

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