Guichard-Combinatorics-Graph-Theory · Problem 1.6.5

Fundamentals

Mathematics — Probability · pigeonhole-principle

Problem

Suppose

(a_1, a_2, \ldots, a_{52})

are integers, not necessarily distinct. Show that there are two,

a_i

and

a_j

with

i \neq j

, such that either

a_i + a_j

a_i - a_j

is divisible by 100. Show that this is not necessarily true for integers

(a_1, a_2, \ldots, a_{51})