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Arithmetic Puzzles Created by Inna Shapiro ©2008 Problem 1 Please, replace the “#” and “&” symbols with digits ## + # & 197 Answer 99 + 9 8 197 Problem 2 Please, replace the “#” and “&” symbols with digits 1### &&& 1 Answer - 1000 999 1 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). 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 Problem 4 Please, replace letters with digits BDCE + B DAE AECBE Answer 5240 +5 2 1 0 10450 Problem 5 Please, replace letters with digits a52b - b 2 5 a 8cdc Answer - 9521 1259 8262 Problem 6 How can you replace “#” and “&” symbols? 1. #### + 1 = 1&&&& 2. 1&&&&&& - 1 = ###### Answers 1. 9999 + 1 = 10000 2. 1000000 – 1 = 999999 Problem 7 Can you change letters ‘a’ and ‘b’ to digits? b aaaa +aaaa aaaa baaaa Answer 2 9999 +9999 9999 29999 Problem 8 Please, replace letters with digits to get the correct answer 7abcdef : 5 = abcdef7 Answer 714285 : 5 = 142857 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? Answer The original number is 45, when Max added 0 he got 405, 45 * 9 = 405 Problem 10 Please add arithmetic signs and parenthesis to get correct answers: 5555=3 5555=4 5555=5 5555=6 5555=7 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