1. Cross-Out

This is a simple two-person game to sharpen your logic skills. On a piece of paper, draw five rows of lines, with one line in the first row, two in the second, three in the third, four in the fourth, and five in the fifth, as seen on the left. Then the players take turns crossing out as many lines in a single row as they wish. The player with the last line left to cross out loses.
Here, for example, the blue player has begun (1) by crossing out two lines from the third row. Each cross-out must be in a single row, it must begin from one end of the row (or where a previous cross-out has ended), and it must eliminate consecutive lines (leaving no uncrossed-out lines in the middle).
Red now takes a turn (2), by crossing out the first line in the fourth row.
Blue responds (3) by crossing out another line in the fourth row, this one one the right side. (As you will learn, only the number--and not the position within the row--of the lines crossed out is significant.)
Now red strikes out the entire fifth row (4), and blue crosses out the remaining two lines in the fourth row (5).
Red eliminates one line in the second row (6), and blue crosses out the only line in the first row (7).
Finally, red crosses out the other line in the second row (9), leaving blue with the last line. Blue loses.

Assignment: Play Cross-Out a few times, until you are familiar with the game. (You can play it via e-mail simply by identifying the row and number of lines on each move, such as "3 from the fourth row," "1 from the third row," "all of the fifth row," and so on.) Then devise a set of instructions on "How to Win at Cross-Out."