MathDB

There are three sticks, each of which has an integer length which is at least

n

; the sum of their lengths is

n(n + 1)/2

. Prove that it is possible to break the sticks (possibly several times) so that the resulting sticks have length

1, 2,\dots, n

.
Note: a stick of length

a + b

can be broken into sticks of lengths

a

and

b

Problem Statement