MathDB

There are

n+1

squares in a row, labelled from 0 to

n

. Tony starts with

k

stones on square 0. On each move, he may choose a stone and advance the stone up to

m

squares where

m

is the number of stones on the same square (including itself) or behind it.
Tony's goal is to get all stones to square

n

. Show that Tony cannot achieve his goal in fewer than

\frac{n}{1} + \frac{n}{2} + \cdots + \frac{n}{k}

moves.
Proposed by Tony Wang

6