by **randomGeek** » Wed Apr 06, 2016 5:06 am

For the $1.27 sequence:

The total value of all pennies on the chessboard is always equal to 2n -1. Hence, on Square1, the total value must be 2(1) - 1 = 1. On Square2, the total value must now be 2(2) - 1 = 3, hence two pennies are added to Square2 to make a total of 3 pennies on the board. On Square 3, the total value must be 2(3) - 1 = 5, so two pennies are put on Square3 to make a total of 5. Thus, 1 penny on Square1, and 2 pennies on all following Squares for a total of 2(64) - 1 = 127.

For the 0.96 sequence:

One penny on every odd numbered square, 2 pennies on every even numbered square, or 1,2,1,2,1,2... for a total of 96.

Moral of the story:

Always request more datapoints!

For the $1.27 sequence:

The total value of all pennies on the chessboard is always equal to 2n -1. Hence, on Square1, the total value must be 2(1) - 1 = 1. On Square2, the total value must now be 2(2) - 1 = 3, hence two pennies are added to Square2 to make a total of 3 pennies on the board. On Square 3, the total value must be 2(3) - 1 = 5, so two pennies are put on Square3 to make a total of 5. Thus, 1 penny on Square1, and 2 pennies on all following Squares for a total of 2(64) - 1 = 127.

For the 0.96 sequence:

One penny on every odd numbered square, 2 pennies on every even numbered square, or 1,2,1,2,1,2... for a total of 96.

Moral of the story:

Always request more datapoints!