Suppose you had 1200 sugar cubes... can you help

[mathchic12]

Suppose you had 1200 sugar cubes. What is the largest cube you can build with the sugar cubes? My brain is fried. I think it would be 10 by 10 by 10 because that's 1000 and 11 by 11 by 11 is 1320 which is too much. Help!

 

[Deleted member 4993]

Suppose you had 1200 sugar cubes. What is the largest cube you can build with the sugar cubes? My brain is fried. I think it would be 10 by 10 by 10 because that's 1000 and 11 by 11 by 11 is 1320 which is too much. Help!

This question is "not well- defined". You could build a sugar cube - with a void inside. In that case you'll look for a solution like a^3 - (a-2)^3 = 1200

Try it - you might like the solution.

If by chance - "cube" in this problem meant "rectangular prism" - then of course there are many answers.

 

[mmm4444bot]

Hi MathChic:

Subhotosh makes a valid point, and I will enjoy thinking about Subhotosh's suggestion later; however, if we assume that the sugar-cube construction is a solid, then your calculation is correct.

The answer is 10 sugar cubes by 10 sugar cubes by 10 sugar cubes.

You wrote,

My brain is fried. I think ... 11 by 11 by 11 is 1320 ...

Your brain is fried. 11^3 = 1331.

~ Mark

 

[Denis]

This question is "not well- defined". You could build a sugar cube - with a void inside. In that case you'll look for a solution like a^3 - (a-2)^3 = 1200

Chicadoo, if you have a hard time "picturing" that, take a 8 by 8 checkerboard: pretend it's made using 64 little cubes.
Now "unglue" these cubes: you now form a "frame" with them.
If you use 17 at top anf 17 at bottom, then you need 17-2 = 15 on each side to finish up the frame: see that?
17 * 2 + 15 * 2 = 34 + 30 = 64 : all 64 have been used.
Once you're "at ease" with this "square" procedure, then apply to "cubes"; it'll be easier...