UCD Openday 2005
Mathematics Problem
You must follow the rules.
Cube and Square
a problem about
colouring without repetition
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A square Q is composed of nine 1cm x 1cm x1cm
coloured blocks (see sketch, Q1 )and has
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3 distinct colours in each of its 3 rows,
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3 distinct colours in each of its 3 columns
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and 3 distinct colours on each of its 2 diagonals
Find the least possible number of distinct colours needed
to construct such a square.
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A cube K is composed of twenty seven 1cm x 1cm x 1cm
coloured blocks (see sketch Q2)
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in such a way that each of the 9 squares found in K
(see sketch) are as in (1)
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and with 3 distinct colours in each of its four superdiagonals
(see sketch).
Find the least possible number of distinct colours needed to construct
such a cube.
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Revised 15 Mar 2005.