Didn't I tell ya not ter tear books?
Number Theory
Level
3
Ani tore out some pages from a book. The number of the first page he tore out was 183 and it is known that the number of the last page he tore out is written with the same digits in some order. How many pages did he tear out?
631
136
135
630
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1 solution
The last page torn out should be even as the alternate pages of a book are odd and even with the odd numbered pages being on the right side. So the last page Ani tore out would have an even number with the digits 1,3 and 8 and should also be greater than 183. The only number satisfying this is 318. So Ani tore out some pages starting from 183 and ending in 318. So he tore out 3 1 8 − 1 8 3 + 1 = 1 3 6 p a g e s .