MathDB

The square

ABCD

is divided into

n^2

equal small (elementary) squares by parallel lines to its sides, (see the figure for the case

n = 4

). A spider starts from point

A

and moving only to the right and up tries to arrive at point

C

. Every ” movement” of the spider consists of: ”

k

steps to the right and

m

steps up” or ”

m

steps to the right and

k

steps up” (which can be performed in any way). The spider first makes

l

”movements” and in then, moves to the right or up without any restriction. If

n = m \cdot l

, find all possible ways the spider can approach the point

C

, where

n, m, k, l

are positive integers with

k < m

. https://cdn.artofproblemsolving.com/attachments/2/d/4fb71086beb844ca7c492a30c7d333fa08d381.png

Problem Statement