Post Aap2usc7C9Fel2Om9I by OscarCunningham@mathstodon.xyz
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 (DIR) Post #Aap2usc7C9Fel2Om9I by OscarCunningham@mathstodon.xyz
       2023-10-15T20:25:50Z
       
       0 likes, 1 repeats
       
       #Mathober #Mathober2023 The prompt for day 11 is 'Quadratic'.When I was a kid, my mum would buy The Guardian newspaper, and along with the crosswords and sudokus there was a section of maths/logic puzzles.I remember one of these puzzles asked the following question: 'Suppose we throw a coin onto a tiled floor. The tiles are squares with side length twice the diameter of the coin. What's the probability that the coin avoids landing on a crack?' (I'm sure they presented it more entertainingly than that.)Now this problem doesn't require you to solve a quadratic. But when I worked out the answer I remember thinking that the probability was much smaller than I expected. It's hard to avoid those cracks!So I thought it might make a fun game. You'd scale up the tiles until there was just less than a 50% chance that the coin missed the crack. People would think it was an easy game, but they'd lose more often than they'd win. (I suspect there is no possibility at all of skillfully controlling the bounces of a metal coin on a hard floor.)To do this you'd have to find the tile size at which there was a 1/2 chance of landing on a crack. This inverse problem *does* require you to solve a quadratic. I remember it as one of the first times I used some 'advanced' maths to solve a problem that I'd thought up myself, rather than one I'd gotten from a book.#Math #Maths #Mathematics