[ Decimal number system ] $[$ Arithmetic. Mental calculation, etc. ]

A part of a book fell out. The first of the missing pages has the number 387, and the number of the last page consists of the same digits but in a different order. How many sheets fell out of the book?
Notice that when a part of a book falls out, the first of the fallen pages has an odd number, and the last one has an even number.

## Solution

When a part of a book falls out, the first of the fallen pages has an odd number, and the last one has an even number (each page is numbered on both sides, and two numbers are required for its numbering). This means that the last digit of the last page number is 8, i.e., the page number is either 378 or 738; but 378 cannot be, since 378 < 387 (the last page cannot have a number smaller than the first). Therefore, the only possibility left is that the last page number is 738. This means that (738 - 386) $: 2=$ 176 sheets fell out of the book. (We divide by two because a sheet is numbered on both sides.)

## Answer

176 sheets.