Numbers in a cube
Source: ToT Junior O Level Autumn 1998
October 5, 2008
geometry3D geometrycombinatorics proposedcombinatorics
Problem Statement
A block is cut up into 8000 non-overlapping unit cubes and a number is assigned to each. It is known that in each column of 20 cubes parallel to any edge of the block, the sum of their numbers is equal to 1. The number assigned to one of the unit cubes is 10. Three slices parallel to the faces of the block contain this unit cube. Find the sume of all numbers of the cubes outside these slices.