Unit Cubes 6 – Uncolored

Probability Level 2

If someone painted the outside of an n × n × n n \times n \times n cube made out of 1 × 1 × 1 1 \times 1 \times 1 unit cubes, and there were 216 unit cubes with no paint on them at all, what is n n ?


The answer is 8.

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Arron Kau by Arron Kau

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2 solutions

Shreya R
May 23, 2014

The number of blocks uncolored is given by the formula ( n − 2 ) 3 { (n-2) }^{ 3 } . Therefore, ( n − 2 ) 3 = 216 { (n-2) }^{ 3 }=216 . Solving, we get n = 8 n=8

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What is the mean of number of blocks

Saloni Singh - 6 years ago
Ashrith Kishore
May 26, 2014

Un painted cubes or inside cube is 216 so cube root of 216 is 6 so outer cube which is painted is 6+2 that is 8

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