A seesaw is a board balanced at the center that children play on. We are going to explore a very special kind of seesaw onto which we put weights. If the seesaw tilts to the left, then all weights move by one meter to the left. Similarly for the right. When a seesaw tilts to one side, any weight at the end of that side will fall off, thus completely changing the torque on the seesaw.
Strainge things can happen. For example, we can arrange a configuration in which a seesaw tilts left, then right, then left again. Further we can think of a game in which each player tries to get as many weights on his or her side as possible. To gain intuition, please look here.
The game works in rounds: all players will be given the total length L of the seesaw board (which will always be an even number), the maximum weight available to the left side player LeftMax , and the maximum to the right side player RightMax . These maximums will both be positive whole numbers.
In each case the player will in fact be given all the weights from 1 kilogram to the maximum allowed. For example if LeftMax is 5, then the Left player will have weights 1, 2, 3, 4, 5.
Next the Left player places weights on the left side of the seesaw at meter locations, but no weight may be placed on top of another.
After Left is done, Right places weights on the Right side with the same restrictions.
Then the seesaw is allowed to tilt one way and the other. The weights that fall to the Left add to the score of Left. The weights that fall to the Right add to the score of Right. If the seesaw ever settles into a balanced state, then that round is over and neither player gets more of a score for that round.
Each team will play a round as Left player and a round as Right player. The team with the greatest total score wins.
Here is the NoTipping implementation from 2021 This is not the same game, because NoTipping has two fulcrums and the rules are different. But perhaps the display will be useful to you.