3

Part of 1981 Bundeswettbewerb Mathematik

Problems(2)

Bundeswettbewerb Mathematik 1981 Problem 1.3

Source: Bundeswettbewerb Mathematik 1981 Round 1

A square of sidelength

2^n

is divided into unit squares. One of the unit squares is deleted. Prove that the rest of the square can be tiled with

L

combinatoricsTrominosquare

Mind Blowing Number Theory

Source: India LIMIT 2021 Sample Set

n = 2^k

. Prove that we can select

n

integers from any

2n-1

integers such that their sum is divisible by

n