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2022 Balkan MO Shortlist
C5
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Part of
2022 Balkan MO Shortlist
Problems
(1)
Tiling a cube
Source: Serbia MO 2023 P2
4/29/2023
Given is a cube of side length
2021
2021
2021
. In how many different ways is it possible to add somewhere on the boundary of this cube a
1
×
1
×
1
1\times 1\times 1
1
×
1
×
1
cube in such a way that the new shape can be filled in with
1
×
1
×
k
1\times 1\times k
1
×
1
×
k
shapes, for some natural number
k
k
k
,
k
≥
2
k\geq 2
k
≥
2
?