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%?
This is just a variation of the Birthday Problem for a calendar with 2315 days. And daily words in place of people. https://en.wikipedia.org/wiki/Birthday_problem
Rather than try to find a calculator that could handle the giant factorials involved, I used my TI84 to make a table.
Recursively u(1)=1, u(n+1)=u(n)(2315-n)/2315
For the probability that there will be NO repeats.
For day 57 this drops below 50%
For day 145 this drops below 1%
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Posted by Jer
on 2022-02-15 09:00:50 |
Solution
