A book with more than 100 pages was torn up by four people, leaving a total of 8037 pages. How many pages does this book have at most?

Tear off 4 sheets, at least 1, 2, 3, 4, 5, 6, 7, 8, with page numbers and =36.

X, X- 1, X-2 ..., X-7, page number at most 8X+28.

There are:

8037+36 & lt； (X+ 1)X/2 & lt； 8037+28+8X

solve

126 <X & lt 135

This book has at most 134 pages.

Sum of four torn pages = (1+134) *134/2-8037 =1008.

For example,109+10+129+130+131+132+/kloc-0.

In addition, the total number of pages in a book is odd, and the number of pages is not necessarily odd. For example, there are 10 pages, and the sum of page numbers =55.

Extended data:

(1) A number minus the sum of two numbers is equal to subtracting each addend in the sum from this number in turn. For example:134-(34+63) =134-34-63 = 37.

(2) A number minus the difference between two numbers is equal to this number minus the minuend in the difference first and then minus the minuend. For example: 100-(32-15) =100-32+15 = 68+15 = 83.

(3) Subtract a number from the sum of several numbers. You can choose any addend to subtract this number, and then add it with the rest addends. For example: (35+17+29)-25 = 35-25+17+29 = 56.

(4) A number subtracts several numbers in succession. You can add all the subtractions first, and then subtract the sum of the subtractions from the minuend. For example: 276-115-85 = 276-(115+85) = 76.

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