185

Part of 1950 Moscow Mathematical Olympiad

Problems(1)

MMO 185 Moscow MO 1950 erase 90 from 1,2,3,...,101 increasing / decreasing

Source:

1, 2, 3, . . . , 101

are written in a row in some order. Prove that it is always possible to erase

90

of the numbers so that the remaining

11

numbers remain arranged in either increasing or decreasing order.

algebracombinatorics