MathDB

A number of

17

workers stand in a row. Every contiguous group of at least

2

workers is a

<span class='latex-italic'>brigade</span>

. The chief wants to assign each brigade a leader (which is a member of the brigade) so that each worker’s number of assignments is divisible by

4

. Prove that the number of such ways to assign the leaders is divisible by

17

.
Mikhail Antipov, Russia

3