Difference between revisions of "2017 AIME II Problems/Problem 14"
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| − | + | ==Problem== | |
A <math>10\times10\times10</math> grid of points consists of all points in space of the form <math>(i,j,k)</math>, where <math>i</math>, <math>j</math>, and <math>k</math> are integers between <math>1</math> and <math>10</math>, inclusive. Find the number of different lines that contain exactly <math>8</math> of these points. | A <math>10\times10\times10</math> grid of points consists of all points in space of the form <math>(i,j,k)</math>, where <math>i</math>, <math>j</math>, and <math>k</math> are integers between <math>1</math> and <math>10</math>, inclusive. Find the number of different lines that contain exactly <math>8</math> of these points. | ||
| − | + | ==Solution== | |
<math>\boxed{168}</math> | <math>\boxed{168}</math> | ||
| + | |||
| + | =See Also= | ||
| + | {{AIME box|year=2017|n=II|num-b=13|num-a=15}} | ||
| + | {{MAA Notice}} | ||
Revision as of 13:02, 23 March 2017
Problem
A 
grid of points consists of all points in space of the form 
, where 
, 
, and 
are integers between 
and 
, inclusive. Find the number of different lines that contain exactly 
of these points.
Solution
See Also
| 2017 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 13 |
Followed by Problem 15 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
