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June 13th, 2015, 01:43 AM   #1
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How many red cube can surround a blue cube?(all equal size)

Question taken from--> https://brilliant.org/profile/calvin...p=3BX9rjPrQ3CM

You have a (solid) blue cube and an unlimited amount of (solid) red cubes, all of which are of the same size. What is the largest number of red cubes that can touch the blue cube along its sides or parts of its sides?

Touching along edges or at corner points do not count.

I tried , i get 20 only but the answer is 24......

let blue cube = B , let red cube = r

Level 1 : (the blue cube is at center and rotated 45°)
$\displaystyle \ \ \ \ r \ \ r \ \ \ $
$\displaystyle \ \ r \ \ r \ \ r \ \ $
$\displaystyle \ \ \ \ r \ \ r \ \ \ $
Level 2 :
$\displaystyle \ \ \ \ \ r$
$\displaystyle \ \ r \ \ \ \ \ r$
$\displaystyle \ \ \ \ \ B$
$\displaystyle \ \ r \ \ \ \ \ r$
$\displaystyle \ \ \ \ \ r$

Level 3 : (same as level 1)
$\displaystyle \ \ \ \ r \ \ r \ \ \ $
$\displaystyle \ \ r \ \ r \ \ r \ \ $
$\displaystyle \ \ \ \ r \ \ r \ \ \ $

total = 7 + 7 + 6 = 20 cubes , how to get 24?
rnck is offline  
 
December 5th, 2015, 04:49 AM   #2
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what about 8 times 3, or 8+8+8
mark eaton24 is offline  
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