This problem was posed by one of our Taster Day attendees, and uses a similar sort of reasoning to the problem in the video.

If you were on a Taster Day and have already solved it, we’d love to hear of any similar problems you have come across – or for you to invent one. Any good problems will be posted together with the solution to the challenge.

Here’s the problem:

I have two blue dice and one red die.

I use the blue die to play a simple game: if I roll a double six, I win. Otherwise, I lose.

I also roll the red die. If I roll a one, I’ll lie about whether I’ve won or lost the game; if I roll any other number, I’ll tell the truth.

 

I just rolled all three dice.

I turn to you and say “I won!”.

What is the probably that I did in fact win the game?