Problem
COM-B1-M05-P008 One Number Divides Another
#8
★★☆☆☆ Level 2 of 5
Prove that among any \(10\) numbers from \(1,\ldots,18\), two are such that one divides the other.
The box is the odd part of a number.
Each number has the form \(2^k m\), where \(m\) is odd. There are only \(9\) possible odd parts in \(1,\ldots,18\). Among \(10\) chosen numbers, two have the same odd part. Then they are \(2^a m\) and \(2^b m\), and the smaller divides the larger.
Classic strong choice of boxes.