Letting it rip
Chin-ying Nehowakizuki got angry while trying to read the AoPS Intro to Algebra textbook, so he ripped several consecutive sheets out of the book. The smallest number on any of the sheets he ripped out was 385 and the largest number is known to be written with the same digits but in different order. How many sheets did Chin-ying Nehowakizuki rip out of his beloved textbook?
The answer is 77.
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1 solution
If Chin-Ying had ripped out pages, odd numbered pages must come on the right of the book, because the smallest number must be on the right of the book. Now, the biggest number must appear on the left of the book, for it to be the largest. Thus, the largest number must be even. The only even combinations with the three digits are 3 5 8 and 5 3 8 . 3 5 8 < 3 8 5 , thus the largest number must be 5 3 8 .
The no.of sides is 5 3 8 − 3 8 5 = 1 5 3 , but the question asked for number of sheets, which would be 2 1 5 3 + 1 = 7 7