It's documented that the daily
WORDLE word comes from a list of 2315 5-letter words and that there is a specific order in which these are being presented for that viral word game. Presumably the sequence was chosen randomly at the "beginning", rather than make a random choice each day from among the 2315. This prevents the same word coming up twice in the first 2315 days of the puzzle.
Suppose however that they had decided to make each day's word selection to be made randomly, without regard to whether the word had been chosen previously. How many days could the set of words for the day run before the probability of a repeat would exceed (a) 1/2, or (b) 99%?
(In reply to
Solution by Jer)
I thought I'd try using Stirling's formula so that I could solve this with a graph.
https://www.desmos.com/calculator/ci22cl1agn
f(x) is the exact formula
g(x) is the approximate logarithm of f(x) using Stirling's formula
h(x) is a more simplified version
You can find the intersections with ln(1/2) and ln(1/100) by clicking them. The solutions are found by rounding up.
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Posted by Jer
on 2022-02-16 11:24:00 |
re: Solution
