Dots To Primes Game

This is a game for any plural number of players.

Materials: Blank pieces of paper, and a grid drawn on tracing paper. The horizontal rows of the grid are labeled in order 1, 2, 3, 4,..., such that there is one number per row.

Players take turns being the offense player.
At the beginning of a round, all of the players take turns placing dots on a blank piece of paper anywhere (anywhere where there isn't already a dot) within a large circle drawn on the paper. The size of the circle is the same each round.
A fixed total number of dots are drawn. This number is the same for all rounds.

After the dots are drawn, the offense player then rotates the tracing-paper grid in any way he/she desires, and places it over the circle of dots such that the circle is completely covered by the grid.

The offense player then reads the vertical positions of the dots from left to right -- relative to the grid. The offense player then reads the vertical positions of the dots from left to right -- relative to the grid. The offense player the forms the "first list" by writing down the numbers of the rows the dots fall into in order from the leftmost dot, relative to the grid, to the rightmost dot.

The offense player then forms a second list of partial sums of the first list.
The offense player starts this second list of numbers by first writing down the first number of the first list of numbers. He/she then adds the next number of the first list to the first number of the second (and of the first) list, and writes down the sum, then continues writing down all the partial sums, summed from left to right, until, finally, the last number in the second list is the sum of all the numbers in the first list.

Then the offense player circles all of the primes in the second list (the list of partial sums). The number of primes is the offense player's score for the round.

Then there is a new round with another offense player. Play continues until each player has been offense the same predetermined number of rounds.

Highest score wins.

Thanks,
Leroy Quet