Thinking Out Loud – EGMO 2013 Problem 2
EGMO 2013, problem 2. Determine all integers \(m\) for which the \(m\times m\) square can be dissected into five rectangles, the side lengths of which are the integers \(1, 2, 3, \dotsc, 10\) in some order.
EGMO 2013, problem 3. Let \(n\) be a positive integer.
EGMO 2015, Problem 5. Let \(m, n\) be positive integers with \(m > 1\). Anastasia partitions the integers \(1, 2, \dots , 2m\) into \(m\) pairs. Boris then chooses one integer from each pair and finds the sum of these chosen integers. Prove that Anastasia can select the pairs so that Boris cannot make his sum equal to \(n.\)