Problem
COM-B1-M05-P010 Sum \(21\)
#10
★★☆☆☆ Level 2 of 5
From \(1,\ldots,20\), \(11\) numbers are chosen. Prove that two chosen numbers have sum \(21\).
Split into pairs \((1,20),(2,19),\ldots,(10,11)\).
There are \(10\) pairs, each with sum \(21\). Since \(11\) numbers are chosen, one pair is fully chosen.
Same idea on a larger set.