Enter the maze

The 10p napkin scam

A tipped over coin jar with 10p coins spilling out

You take a napkin and fold it into a perfect square. Pop it on the table and dump a load of 10p pieces on the table beside it. Challenge your friend to a dynamic game of wits and cunning. One by one each of you will place a 10p onto the napkin. The first person who can’t place their 10p piece on the napkin without going over the edge loses. Simple game, simple rules, and a simple way to always win this animated game of strategy.

Two important tricks will ensure your victory in this classic deterministic algorithm computational scam. Yes, it’s a hustle, so use it with care!

Do unto others

Its all about matching moves. Mathematicians would call it symmetry, psychologists would call it mirroring, computer scientists would call it set x=y. Get the first part right and victory has to follow. It’s totally predictable.

Step by step

The first step to ensure victory is a little sneaky, even though your opponent will never spot it. Make sure that when you fold the napkin, you fold it into a square and that you know where the exact centre is. Here’s a hint: if you folded your paper twice diagonally to make it into a square, it will be where the two diagonals cross.

Next give your opponent the chance to go either first or second. Their free decision on this determines your next move. This is called setting the initial conditions. Any computer program needs to be initialised – the values of the core data need to be set before the program can run – but here there are slightly different conditions depending on what your opponent decides. Don’t worry, they won’t notice this part either.

IF they decide to go first THEN pretend you ‘forgot’ one other rule. Tell them you need to place a 10p coin exactly over the middle of the square, then do exactly that.

IF they decide to go second THEN place your first coin exactly on the centre. Either way, you’ve ended up with a coin right in the centre for your opponent’s first move.

You win already!

When you get to this point, you’ve already won. How is that possible just by controlling the position of the first coin placed? Because the game involves turn taking, you have now set up a process that ensures that for every coin they subsequently place you can place a coin in exactly the same mirror position- they place a coin at the top of the napkin, you place your coin opposite at the bottom of the napkin in the same place and so on. You have ensured that from the first move onward any move your opponent makes can be identically mirrored by you onto another empty part of the napkin. They will be the first to arrive at a move when they need to go off the napkin so you win.

The scam of a deterministic algorithm

After the ‘right’ first move the rest, including your victory, must follow by the rules of the game. Computer scientists would call this a deterministic algorithm, because there is no random chance involved. So long as the initial conditions are correct, and you mirror your opponent’s moves, there is no way for them to win. Given a particular input it will always produce the same output, so enjoy!