Difference between revisions of "2021 Fall AMC 10A Problems/Problem 24"
Arcticturn (talk | contribs) (→Solution) |
|||
| Line 5: | Line 5: | ||
==Solution== | ==Solution== | ||
| + | Since we want the sum of the edges of each face to be <math>2</math>, we need there to be <math>2</math> <math>1</math>s and <math>2</math> <math>0</math>s. Through experimentation, we find that the <math>1</math>s and <math>0</math>s must be adjacent to each other on the edges. | ||
| + | |||
| + | I am still working on the solution - in the meantime PLEASE DO NOT EDIT. | ||
| + | |||
| + | ~Arcticturn | ||
==See Also== | ==See Also== | ||
{{AMC10 box|year=2021 Fall|ab=A|num-b=23|num-a=25}} | {{AMC10 box|year=2021 Fall|ab=A|num-b=23|num-a=25}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 19:55, 23 November 2021
Problem
Each of the 
edges of a cube is labeled 
or 
. Two labelings are considered different even if one can be obtained from the other by a sequence of one or more rotations and/or reflections. For how many such labelings is the sum of the labels on the edges of each of the 
faces of the cube equal to 
?
Solution
Since we want the sum of the edges of each face to be , we need there to be s and s. Through experimentation, we find that the s and s must be adjacent to each other on the edges.
I am still working on the solution - in the meantime PLEASE DO NOT EDIT.
~Arcticturn
See Also
| 2021 Fall AMC 10A (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 AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
