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Putnam
1952 Putnam
A6
A6
Part of
1952 Putnam
Problems
(1)
Putnam 1952 A6
Source:
5/29/2022
A man has a rectangular block of wood
m
m
m
by
n
n
n
by
r
r
r
inches (
m
,
n
,
m, n,
m
,
n
,
and
r
r
r
are integers). He paints the entire surface of the block, cuts the block into inch cubes, and notices that exactly half the cubes are completely unpainted. Prove that the number of essentially different blocks with this property is finite. (Do not attempt to enumerate them.)
Putnam