Let’s look at another riddle!
To be honest, this riddle is by far one of my favorites (So far!).
Question: While walking in an amusement park you stumble upon one of those carnival games. The sign on the booth reads “Win 1 million dollars”. Naturally, your excited. You walk inside and ask what you must do inorder to win the grand prize. The person behind the counter responds:
In front of you is a box with 4 corners. I will shut all the lights in the booth and place a quarter in each of the corners of the box. Each quarter will have a 50% chance of being placed face-up and a 50% chance of being placed face-down. Due to the darkness, you have no clue which quarters are oriented face-up and which face-down. Once the board is set up, the game begins.
The game consists of 3 recurring stages.
Stage 1: Reorientation. In this stage you will have a chance to flip over whichever quarters you want. Recall that you only know which quarters your filpping, not their starting or new orientations
Stage 2: The Ask. Once your satisfied with your flips you will ask the booth person if the quarters all show the same orientation (All are face-up or all are face-down). The booth person will let you know
Stage 3: Win or Rotate. If the booth person responded with “YES” all are face-up/face-down, YOU WIN THE GRAND PRIZE!!!!!. In any other case, the booth person, after responding “NO” will rotate the box that contains the quarters some multiple of 90-Degrees. Note: The rotation is random each turn
These 3 stages repeat until you WIN
You’re eager to play, because you’d love to win but there is one problem. You know that if you start, you’ll never leave until you win. Therefore you only want to play if you KNOW FOR CERTAIN you will win. You also don’t want to play if you think the answer will take an infinite number of rounds (Because than you’ll never get a chance to leave!!). So, is it worth it to play or not? In other words, can you guarentee that you can get all quarters face-up or face-down in a finite number of moves while playing by the rules of the game?
Answer to come. Think about it