MathDB

The game of

pebbles

is played on an infinite board of lattice points

(i,j)

. Initially there is a

pebble

(0,0)

. A move consists of removing a

pebble

from point

(i,j)

and placing a

pebble

at each of the points

(i+1,j)

and

(i,j+1)

provided both are vacant. Show taht at any stage of the game there is a

pebble

at some lattice point

(a,b)

with

0 \leq a+b \leq 3

Problem Statement