Gregory Bonik gregory at bonik.org
Fri Apr 30 21:18:47 BST 2010

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Status in “gbrainy” package in Ubuntu: New

Bug description:
Binary package hint: gbrainy

"How many cubes do you count in the figure below? (not counting the figure)",

and the picture of a big cube subdivided into n^3 small cubes follows (see attachment). The number n is either 4, 5, or 6. GBrainy says that for each n the correct answer is n^3 (i. e. 64 for n = 4, 125 for n = 5 and 216 for n = 6), but obviously that's wrong.

There are also sub-cubes of sizes 2x2x2, 3x3x3 and so on. For example, in the case of n = 4, one can find 99 cubes:

8 = 2^3 cubes of size 3x3x3,
27 = 3^3 cubes of size 2x2x2
and 64 = 4^3 cubes of size 1x1x1.

So, for an arbitrary n the correct answer is 1^3 + 2^3 + ... + n^3. In particular, the answer for n = 5 is 224, the answer for n = 6 is 440, and, as already mentioned, the answer for n =4 is 99.