2

Part of 1928 Eotvos Mathematical Competition

Problems(1)

numbers 1-n on the circumference of a circle

Source: Eotvos 1928 p2

Put the numbers

1,2,3,...,n

on the circumference of a circle in such a way that the difference between neighboring numbers is at most

2

. Prove that there is just one solution (if regard is paid only to the order in which the numbers are arranged).