Which color is larger?

Algebra Level 3

Given a 7x7x7 cube as seen in the picture. Two small cubes of the same color don’t share a common face. Which color of cubes is greater the black or the white?

The color of the white cubes is greater than the color of the black cubes There are equal number of white and black cubes. The color of the black cubes is greater than the color of the white cubes

Hana Wehbi by Hana Wehbi , 51, USA

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2 solutions

Geoff Pilling
Nov 6, 2018

Just one comment... You might want to change the solutions to say "The number of black/white cubes is greater ... "

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I can't edit the answers. Is there is anything unclear somewhere?

Hana Wehbi - 2 years, 7 months ago
Parth Sankhe
Oct 30, 2018

Counting the "landlocked" 5×5 grids on each face, we'll have 13 W and 12 B for each face.

Then counting the edges gives us 24+8=32W and 24+12=36 B.

Adding both up, we notice that there are 2 more white cubes than black cubes.

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