left column. Now we make the same moves we did for addition. Replace two counters on a square with one to its left. If the square is on the left column, replace two counters with one above it. Recall that the value of a square doubles if you move up, so this does not change the value on the grid. Let's first replace the two counters on the second square at the bottom with one to its left which leaves two counters at the corner. Finally, replace the two counters on the corner with one above it and "read off" the binary number in an L-shaped fashion, starting from the top left down to the bottom left corner, and then over to the bottom right. Read the counters along the L but do not double count the corner square. You will read the binary result 11000110 = 198 which is indeed 22*9. Why can we read the binary number in this L-shaped fashion? The bottom row is of course just the first six powers of two, but notice that the leftmost column has the next five powers of two. So we can directly read off an 11 digit binary number from the L-shaped set of 11 squares that lie along the left and bottom sides of the grid. Our small 6x6 grid can only multiply numbers each up to 63, and in general an nxn grid can multiply two numbers each up to 2n-1. This scales very fast, so board with 20 numbers per side, for instance, can multiply numbers each up to a little over one million. Division Martin Gardner presented a slightly easier to understand version of Napier's division method, which is what is shown here. Division works pretty much the reverse of multiplication. Say we want to divide 485 by 13. First place counters for 485 (= 111100101) along the bottom edge and mark 13 (= 1101) along the right edge. To save space, we'll just look at a rectangular portion of the board because that's all we actually use. Starting from the left, the game is to move counters diagonally into "columns of divisors" (that is, with one counter on each row marked with a 1 from the divisor.) Let's demonstrate this with the leftmost block of counters. Now the next block of counters we might try would begin with the leftmost counter on the bottom,