1988 AJHSME Problems/Problem 16

From AoPSWiki

Problem

Placing no more than one $\text{X}$ in each small square, what is the greatest number of $\text{X}$ 's that can be put on the grid shown without getting three $\text{X}$ 's in a row vertically, horizontally, or diagonally?

$\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 5 \qquad \text{(E)}\ 6$

Solution

By the Pigeonhole Principle, if there are at least $7$ $\text{X}$ 's, then there will be some row with $3$ $\text{X}$ 's. We can put in $6$ by leaving out the three boxes in one of the main diagonals.

$\rightarrow \boxed{\text{E}}$

1988 AJHSME (Problems • 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

Personal tools

Navigation

Search

Toolbox

1988 AJHSME Problems/Problem 16

From AoPSWiki

Problem

Solution

See Also