Question

The left and right page numbers of an open book are two consecutive integers whose sum is 87.

Answer 1

Left page numbers are always even and right page will have a number 1 greater that the left. so its not possible to have a sum of 87.
If even page is 2n then right page = 2n + 1:-

2n + 2n + 1 = 87

4n = 86

n = 86 / 4 = 21.5 and 2n = 43 but left page is even so its not possible to have a sum of left + right = 87.