# The King and the Mathematician

**Algebra**Level 2

The man who happened to be a mathematician thought a little bit and said the following:

"Bring in a big piece of rug with an \(8\times 8\) grid in it. Start from the top left square, put one dollar in that square. Put two dollars in the square next to it and then double of that, four dollars, in the next square and so on, and when you reach the end of the first row, continue on to the next row, doubling the amount every time as you move to the next square, all the way until the \(64^\text{th}\) square at the bottom right."

The king thought for a second. The first square will take one dollar, the second two dollars, the third, four dollars, and next 8 dollars, and then 16 dollars, and then 32 dollars, 64 dollars, 128 dollars, 256 dollars, and so on. That's not too bad. I can do it.

The king agreed. What happened next?