To whom it may concern. Here is a game, Leap Frog, which may not be original. It is played on a strip of squares. A move is to place a bean on an unoccupied square. So far we have one of the many manifestations of She-Loves-Me-She-Loves-Me-Not, but there is a second type of move. A player may jump a bean onto an unocupied square, provided there is at least one intervening square and all such intervening squares are occupied by beans. To ensure that the Ending Condition is satisfied, we will say that such jumping moves may not be reversed. If you make that ``may not be IMMEDIATELY reversed'' or ``may not be reversed by the opposite player'' then these versions may be of interest, but I suspect that ties occur for n > 5. For 0 < n < 5 the game is equivalent to S-L-M-S-L-M-N, since jumping moves need not arise. For example, for n = 4, 1 & 3 are good replies to one another, as are 2 & 4. n = 5 is an N-position. For example, placing a bean on square 3 wins. The moves 1 & 5 are good replies to each other, while 2 (or 4) can be met by 1 (or 5), since the jumping moves 2 to 4 or 1 to 4 are met by the jump 3 to 5. n = 6 is beginning to get difficult by hand. Over to you! Fame & fortune await a complete analysis! R.