4

Part of 1981 Swedish Mathematical Competition

Problems(1)

cube of side 5is divided into 125 black and white unit cubes

Source: 1981 Swedish Mathematical Competition p4

5

is divided into

125

N

of the small cubes are black and the rest white. Find the smallest

N

such that there must be a row of

5

black cubes parallel to one of the edges of the large cube.

combinatorial geometrycombinatorics