Enigmatic Code

Programming Enigma Puzzles

Puzzle #05: Murphy’s law of socks

From New Scientist #3232, 1st June 2019 [link] [link]

I am convinced that my washing machine eats socks. Every time I wash a load, another sock disappears. Last week I ran out of socks, so I bought myself three new pairs.

What is the chance that, after my first three washes, I will be left with three odd socks? Indeed, what is the chance that I will have even one pair intact?


One response to “Puzzle #05: Murphy’s law of socks

  1. Jim Randell 1 June 2019 at 11:28 am

    Assuming each of the three pairs is distinguishable (perhaps each pair is a different colour), and all socks are washed together (6 in the first wash, 5 in the second wash, 4 in the third wash).

    The first wash destroys one of the 6 socks. In the second wash there is a 4/5 chance that a different colour sock is destroyed. And in the third wash there is a 2/4 chance that one of the remaining pair will be destroyed.

    The probability that three odd socks remain after the three washes is therefore: (4/5) × (2/4) = 2/5, or a 40% chance.

    So there is a 60% chance that this doesn’t happen and one complete pair survives the first three washes.

    It is probably better to buy three identical pairs of socks, and then you are guaranteed to have a usable pair after 3 (and even after 4) washes.

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