Problem
COM-B1-M05-P018 Two Consecutive Numbers
#18
★★★☆☆ Level 3 of 5
From \(1,\ldots,100\), \(51\) numbers are chosen. Prove that two chosen numbers are consecutive.
Split the numbers into pairs \((1,2),(3,4),\ldots,(99,100)\).
There are \(50\) pairs of consecutive numbers. Since \(51\) numbers are chosen, one pair is fully chosen. These two numbers are consecutive.
Intervals as boxes.