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Mathematicians' Casino

Puzzle 5: The Rule-ette Wheel

Difficulty:
Fun:
(based on 17 votes)

Heading deeper into the Mathematicians' Casino, you come to the Rule-ette Wheel. It's similar to a regular roulette wheel, with some slight differences. The slots on the wheel consist of all of the whole numbers between 0 and 20, inclusive. 0 is green. All other even numbers less than or equal to 10 are red, as are all odd numbers greater than or equal to 11. All other numbers are black. You can place a bet on a specific number, or on Even or Odd, or on Prime or Non-Prime. The biggest difference is that the wheel is rigged, so that the following four rules are always followed:

  1. If the ball lands on a black number, then on the next spin the ball must land on a red number.
  2. If the ball lands on an even number, then on the next spin the ball must land on an odd number.
  3. If the ball lands on a non-prime number, then on the next spin the ball must land on a prime number.
  4. The absolute difference between the numbers landed on during any two consecutive spins must always be greater than 5.
1. The ball just landed on 18. On what number do you place your bet for the next spin?

2. The ball just landed on a black number, but you didn't see which one. You do know that on the previous spin, the ball had landed on 0. Where do you place your bet for the next spin: Even, Odd, Prime, or Non-Prime?

3. The ball just landed on a black even number, but you didn't see which one. On the previous spin, the ball had landed on 19. On what number do you place your bet for the next spin?

4. The ball just landed on a black number, but you didn't see which one. On the previous spin, the ball had landed on an even number, but again you didn't see which one. The spin before that, the ball had landed on 9. Where do you place your bet for the next spin: Even, Odd, Prime, or Non-Prime?

5. On which of the following numbers should you NEVER place a bet: 12, 13 or 14?


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