Do you know the game Concerto? I did not. Just learnt about it today. The game goes roughly this way –
You start with a grid of squares – can be as big as you want it to be.
Now two players take turns to draw lines. Each turn can draw a line on any of the sides of any of the grid squares – provided somebody had not drawn there already – and it can be of the length of one side at a time only.
(You might remember a variation of this game where anytime somebody completes a grid square, he/she claims that square and in the end you count up who got how many).
However, in this game, anybody who completes a shape – any shape – entirely by his/her own lines only – wins. Note that it does not have to be a square or rectangle – it can be any shape. Also there might be lines drawn inside the shape by any of the players – it does not matter. It just needs to be a completed shape with one player’s lines only.
Look at the picture below as an illustration. The player with lines with black tips wins. Think of the shape comprising the four squares marked with red blobs – that is a complete shape built by the black tip lines only.
Here is the question. Just like the second player in a game of tic tac toe can always prevent the first player from winning, in this game too, the second player can come up with a strategy that will ensure that the first player can never win regardless of how big the grid is.
Can you come up with such a strategy?
(Send me PM with your answers; I will publish your correct answers in the Comments section later)