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June 13th, 2015, 12:43 AM  #1 
Senior Member Joined: Apr 2010 Posts: 128 Thanks: 0  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? 
December 5th, 2015, 03:49 AM  #2 
Senior Member Joined: Nov 2015 From: usa Posts: 152 Thanks: 0 
what about 8 times 3, or 8+8+8


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