# GeekDad Puzzle of the Week – Backsplash Backlash

As we enter week two of our kitchen renovation project, my wife Allison and I have decided that some decisions are joint decisions (we had to agree on which model fridge to purchase) and some are single-spouse decisions (I got to decide how to rewire sockets, Allison selected the cabinets.)

The challenges come when one partner thinks a joint decision is single-spouse, or vice-versa. When laying out a grid for the backsplash we selected, I thought it was reasonable to measure and mark the grid down, then across; Allison suggested I measure and mark across, and then down. “Good thing that there are only two ways to do this,” I said, and then started thinking…

If the backsplash were simply a 3″ x 3″ grid, there would be some ten ways to mark off each horizontal and vertical measurement:

However, our backsplash is a little larger — it’s 12″ x 120″. This week’s assignment, if you choose to accept it, is to determine the number of distinct ways we can mark off or traverse the 12″ x 120″ grid, as shown above. So that calculating technology is not a deciding factor, feel free to round to the nearest quadrillion. As always, send your answers in to GeekDad Central, and all reasonably correct entries will be put into a hat for a chance at this week’s \$50 ThinkGeek Gift Certificate.

Good luck, and happy puzzling!