1988 AJHSME Problems/Problem 16: Difference between revisions
5849206328x (talk | contribs) mNo edit summary |
No edit summary |
||
| Line 26: | Line 26: | ||
{{AJHSME box|year=1988|num-b=15|num-a=17}} | {{AJHSME box|year=1988|num-b=15|num-a=17}} | ||
[[Category:Introductory Combinatorics Problems]] | [[Category:Introductory Combinatorics Problems]] | ||
{{MAA Notice}} | |||
Latest revision as of 22:55, 4 July 2013
Problem
Placing no more than one 
in each small square, what is the greatest number of 's that can be put on the grid shown without getting three 's in a row vertically, horizontally, or diagonally?
![[asy] for(int a=0; a<4; ++a) { draw((a,0)--(a,3)); } for(int b=0; b<4; ++b) { draw((0,b)--(3,b)); } [/asy]](http://latex.artofproblemsolving.com/1/1/6/1161c2f219124fd219c171f81bebebb89efeb9a7.png)
Solution
By the Pigeonhole Principle, if there are at least 
's, then there will be some row with 
's. We can put in 
by leaving out the three boxes in one of the main diagonals.
See Also
| 1988 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 15 |
Followed by Problem 17 | |
| 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 | ||
These problems are copyrighted © by the Mathematical Association of America. 
