Difference between revisions of "1991 AJHSME Problems/Problem 24"
5849206328x (talk | contribs) (Created page with '==Problem== A cube of edge <math>3</math> cm is cut into <math>N</math> smaller cubes, not all the same size. If the edge of each of the smaller cubes is a whole number of cent…') |
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Latest revision as of 00:08, 5 July 2013
Problem
A cube of edge 
cm is cut into 
smaller cubes, not all the same size. If the edge of each of the smaller cubes is a whole number of centimeters, then 
Solution
If none of the cubes have edge length 
, then all of the cubes have edge length 
, meaning they all are the same size, a contradiction.
It is clearly impossible to split a cube of edge into two or more cubes of edge with extra unit cubes, so there is one 
cube and 
unit cubes.
The total number of cubes, , is 
.
See Also
| 1991 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 23 |
Followed by Problem 25 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
