You've just started a job installing a new type of hexagonal bathroom tile. These special tiles lock into one another, making installation a snap. However, this means that the tiles must be connected in order of their color: blue, green, peach, blue, green, peach, etc. . . .

For each job, you're given a plan with some specifications about the bathroom. The home owners may have conferred with the interior decorator about the price of certain rows of tiles (blue tiles are $1, green tiles are $2, and peach tiles are $3), while the site coordinator may have assigned someone to lay down a few tiles to get you started. You don't have to use one of those tiles as the starting tile, or one of any particular color, but once you've laid down the first tile, they must go in the order blue-green-peach.

Also noted on the plan is the tile closest to the door. Since the cement used to attach the tiles to the floor takes twenty-four hours to set, you need to lay down the tile closest to the door last (otherwise you will have painted yourself into the proverbial corner).


Here's an example:


You don't necessarily need to start with the green tile, but it will need to be connected to the others in the order blue-green-peach. Also note that the tiles in the bottom row need to add to $7 and that the tile in the upper left-hand corner must be laid last.

With the tiles at hand, there are two ways to make a $7 row:



Unfortunately, the one on the left doesn't include the necessary green tile that's already been cemented down. We'll have to use the tiles on the right, two green tiles and a peach tile. But should the peach tile go on the far right (as shown) or on the far left?

If we try the far right arrangement, we can lay out the tiles in the blue-green-peach order, like this:



The problem here is that we'd have to start with the blue tile at the door, and we'd wind up stuck in the corner with the peach tile. We can't lay down the tiles in the reverse order (peach-green-blue) to end up at the door.

Instead, we can try the other bottom row arrangement:



Now we have to start with a green tile, but this does follow the blue-green-peach order, and we finish at the door.



Last updated: September 1, 2004
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