J&T TILING COMPANY ONLY TILE SQUARE AREAS AND USE ONLY SQUARE TILES. THEY ALSO ONLY USE ONE PATTERN. ANN PLACES THE CENTER WITH WHITE TILES. BEN COMES ALONG AND BOARDERS THE AREA WITH GRAY TILES. HOW MANY BOARDER TILES ARE NEEDED FOR A 20x20 AREA/? FOR A KxK AREA?

Well, one would think the full 20 would be needed for the first opposing sides (whether top and bottom, or left and right) and 18 would complete the interior of the other sides of the border, so (20 x 2) + (18 x 2) or 40 + 36 which =

**76**. Our generic formula would then be (K x 2) + ((K-2) x 2) = border tiles. If you need to simplify that, it could be 2K + 2k-4, or**4k-4**so for our original 20 x 20, it would be 4(20)-4 or 80 - 4 which is again,

**76**.

## Comments

upon completion.20 x 20 centerof white tiles, and THEN the border is added,the formula becomes,

4K PLUS 4