<p>On a square gameboard that is divided into n rows of n squares each. k of these squares lie along the boundary of the gameboard. Which of the following is a possible value of k?</p>
<p>A) 10
B) 25
C) 34
D) 42
E) 52</p>
<p>PLease can anyone explain how to approach this problem>?</p>
<p>Is the answer E?</p>
<p>Here's how I did it:</p>
<p>So it's a square with n-dimension sides. k is the perimeter so it's going to be 4n, or k=4n. Only E is a multiple of 4, thus the answer is E.</p>
<p>I'm not sure it it's right though. :)</p>
<p>I opened up Microsoft Word and counted the # of squares for tables of increasing size, and your logic checks out.</p>
<p>I agree with E.</p>
<p>assuming the board is square, number of squares on gameboard: N^2
anything that's not on the outer edge of the square is (N-2)^2</p>
<p>N^2-(N-2)^2
gives you 4n-4 assumming n is a whole number.
E is the only answer.</p>
<p>^very clear solution.</p>
<p>A slightly different approach:
remove the corner squares; there are n-2 left on each side, total 4(n-2); add 4 corner squares back, 4(n-2)+4=4n-4. Only E fits.</p>