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If number of cubes painted with colour 3 is 217 then how many cubes are painted with colour5

Correct Answer: 127

Explanation:

Consider the 1st step, initial number of cubes N3 after removal of 1st set of coloured cubes number of cubes left out is (N - 1)3 hence number of cubes removed in 1st step (i.e with colour 1) is
N3 - (N - 1)3 = 3N2 - 3N + 1
Similarly number of cubes removed in 2nd step (i.e with colour 2) is
Similarly number of cubes removed in 3rd step is (i.e with colour 3) and so on.
= 3(N - 1)2 - 3(N - 1) + 1
Number of cubes remaining after 1st step is (N - 1)3
Number of cubes remaining after 2nd step is (N - 2)3 and so on.
From the given condition
Number of cubes removed in 3rd step (i.e with colour 3) is = 3(N - 2)2 - 3(N - 2) + 1 = 217 hence N = 11 So number of cubes with colour 5 is = 3(N - 4)2 - 3(N - 4) + 1 = 127


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