Backwards Reasoning in Game Theory

The key to solving this game-theory puzzle is to use backwards reasoning.

Think about the last but one turn.  If the opposing team was left with 4 flags on it’s last turn, it would have to take 1, 2 or 3. which would allow the winning team to take the remaining flags. So if on your turn you can ensure they will end up with 4 flags you are guaranteed to win.

This same reasoning can be applied to the the turn before that, and the turn before that, and so on.

How do you make sure that the opposing team has 4 flags remaining on their last turn?

You need to leave 4 flags on your opponent’s last turn (L), and 8 flags on their next-from-last (L-1) to ensure that you can leave 4 flags next turn, and 12 flags on their next-from-next-from-last (L-2) and 16 flags on their L-3 turn, and 20 flags on their L-4 turn.

If you start with 21 flags, you therefore need to remove just 1 flag to force this winning strategy on your opponent!

With 21 flags in the field, the first team has a sure win if they hit every target number (4,8,12,16,20) for each step of the process.

Mindware Strategy Application

Imagine the desired end result involving an interaction with someone else.  Think of the previous ‘turn’ that would lead to that end result. Now think of what you could do prior to that point to ensure that this set of conditions is attained. This is the kind of reasoning you need to apply to use this kind of problem solving by analogy to other areas of your life.