perplexus.info :: Probability : Ducks in a pond

Ducks in a pond (Posted on 2023-01-24)

3 ducks have landed in a circular pond. What is the probability there is a diameter such that the semicircle on one side contains all of them?

Repeat for 4 ducks.

Note: consider the ducks to be randomly chosen points in a circle.

No Solution Yet Submitted by Jer

Rating: 5.0000 (2 votes)

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The duck sequence

| Comment 13 of 17 |

This is a cool puzzle. You should submit the sequence of probabilities for n ducks on OEIS. It could be called "the duck sequence". It would start 1, 1, 3/4, 1/2, ... It would be very fun.

Posted by Math Man on 2023-01-25 15:18:09

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