Puzzles:-

Some puzzles intended to illustrate some topics in reasoning, mainly uncertainty.

  • Multiple choice paradox: illustrating non-numeric probabilties.
  • Urns with uncertain contents: is the likelihood always precise?
  • Tennis: is ‘probability is just a number’ valid for games?
  • Medical treatment: does knowing that a disease has 10 different variants make a difference?
  • Bayes’ inspiration: from observing a court or experiments with balls?
  • Car choice: to what extent should you be influenced by general statistics?
  • Coin toss: can tossing a coin be better than having a choice?
  • Coin fairness: does a run of Heads suggest that the coin is not fair?
  • Intelligence-led: Intelligent? Are we getting it right?
  • Unbirthday ‘paradox’. Can some standard assumptions be biased?
  • Cab accident. Are the usual assumptions always justified?
  • Disease. Should you always take medical statistics at face value?
  • Flood risk. Should you assume that your insurance company has calculated your premium using the appropriate formula?
  • Sweets. A popular puzzle, with a critique of the principle of indifference and Bayes’ rule.
  • Cakes. How to divide cakes, given uncertain information.
  • Petty theft. How to interpret evidence and ‘causality’?
  • Probability Question: How to answer questions about probability.
  • Rainbows: What, pragmatically, can we say about their location?
  • Gym: What can we say about the probability of a member coming tonight, given an log of all gym activity?
  • Coincidence (cycling). A British exam question: not as simple as it looks?
  • Weather forecasting. A British exam question: mathematics versus meteorology.
  • Marmalade. What is it? Can you make sense of it as a word?

I intend to produce more. Suggestions welcome, either for puzzles or topics.

These puzzles are not intended to have some definite ‘correct’ solution that can be solved by ‘hard thought’ or advanced methods, nor even to test ingenuity or ‘knowledge’. Rather, the intention is that however you approach them, some of them should provide something ‘to be perplexed about’, to illustrate uncertainty, especially the unavoidable ‘radical’ kind. In this, it follows the approach of Dodgson.

Lets this lead to a cynicism about the human ability to know anything, perhaps mathematical logic, as in du Sautoy or a textbook by Crossley will provide some clues?

See Also

The sleeping beauty problem (strictly for the brave).

Dave Marsay

15 Responses to Puzzles:-

  1. Pingback: Anyone for Tennis? « djmarsay

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  15. Pingback: Flood Risk Puzzle | djmarsay

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