Question

Show that if any five numbers from 1 to 8 are chosen, then two of them will add up to 9. 

Answer 1

The sets which add upto 9 are {1,8}, {2,7}, {3,6}, {4,5} .

By Pigeonhole principle, if we have to choose five numbers then we must take at least two numbers belonging to one set.

Thus two of five numbers will definitely add upto 9.