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National and Regional Contests
Iran Contests
Iran MO (1st Round)
2018 Iran MO (1st Round)
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Part of
2018 Iran MO (1st Round)
Problems
(1)
Least number of plates - Iran First Round 2018, P2
Source:
3/6/2021
A factory packs its products in cubic boxes. In one store, they put
512
512
512
of these cubic boxes together to make a large
8
×
8
×
8
8\times 8 \times 8
8
×
8
×
8
cube. When the temperature goes higher than a limit in the store, it is necessary to separate the
512
512
512
set of boxes using horizontal and vertical plates so that each box has at least one face which is not touching other boxes. What is the least number of plates needed for this purpose?
counting
combinatorics