My friend, while we played tetris, offered me this problem:
Suppose we are playing Netris, an edited versiom of tetris. The field is 7 units long and infinitely tall, with a bottom. The only piece is a 3x1 block which can be flipped so it is 1x3. We earn a point when a row of 7 spaces is filled. Tetris rules apply: when a block falls, if any part of the block hits a square from another block (they can slide past each other) or hits the ground, the block freezes in place.
Unfortunately, we have already put in an arbitrary amount of pieces arbitrarily, and we cannot see where the pieces are.
What is a strategy such that we can announce we have earned at least one more point and know that we are right?
I have no idea how to solve this.
A simple strategy :
Play this sequence of moves:
Then no matter what's the initial state of the game, you'll earn a point at move l or before
The same idea can be used to give an optimized version :