Solution to Puzzle #105: The 150 Year Old Puzzle

This was indeed a more difficult puzzle than it appeared and for a change I did not get any correct solution. One realises that after trying a few combinations for the first 2-3 days, one invariably gets stuck in a hole. This puzzle had gone viral after it was first published, partially just due to its simplicity.

Here is one of the answers to the puzzle, the original source claims that there are seven solutions.

It turns out that there are essentially seven different solutions to Kirkman’s original schoolgirl problem; here’s one of them (All names of course are made up).

Monday:
Annabel-­‐‑Bertha-­‐‑Clarissa
Dora-­‐‑Ermengarde-­‐‑Fanny
Gertrude-­‐‑Harriet-­‐‑Irene
Josephine-­‐‑Katie-­‐‑Louisa
Mabel-­‐‑Nettie-­‐‑Olive

Tuesday:
Annabel-­‐‑Dora-­‐‑Gertrude
Bertha-­‐‑Ermengarde-­‐‑Harriet
Clarissa-­‐‑Louisa-­‐‑Olive
Fanny-­‐‑Josephine-­‐‑Nettie
Irene-­‐‑Katie-­‐‑Mabel

Wednesday:
Annabel-­‐‑Josephine-­‐‑Mabel
Bertha-­‐‑Katie-­‐‑Nettie
Clarissa-­‐‑Fanny-­‐‑Irene
Dora-­‐‑Harriet-­‐‑Louisa
Ermengarde-­‐‑Gertrude-­‐‑Olive

Thursday:
Annabel-­‐‑Ermengarde-­‐‑Katie
Bertha-­‐‑Fanny-­‐‑Louisa
Clarissa-­‐‑Gertrude-­‐‑Mabel
Dora-­‐‑Irene-­‐‑Nettie
Harriet-­‐‑Josephine-­‐‑Olive

Friday:
Annabel-­‐‑Harriet-­‐‑Nettie
Bertha-­‐‑Irene-­‐‑Olive
Clarissa-­‐‑Dora-­‐‑Josephine
Fanny-­‐‑Gertrude-­‐‑Katie
Ermengarde-­‐‑Louisa-­‐‑Mabel

Saturday:
Annabel-­‐‑Fanny-­‐‑Olive
Bertha-­‐‑Dora-­‐‑Mabel
Clarissa-­‐‑Harriet-­‐‑Katie
Ermengarde-­‐‑Irene-­‐‑Josephine
Gertrude-­‐‑Louisa-­‐‑Nettie

Sunday:
Annabel-­‐‑Irene-­‐‑Louisa
Bertha-­‐‑Gertrude-­‐‑Josephine
Clarissa-­‐‑Ermengarde-­‐‑Nettie
Fanny-­‐‑Harriet-­‐‑Mabel
Dora-­‐‑Katie-­‐‑Olive

For the avid puzzlers/ mathematicians, one can see that there can be a more generic version of this puzzle where there are n ladies, who go out in pairs of m each (n is divisible by m) and do this for d days. If you are interested, please refer to the following link:

http://www.wired.com/2015/06/answer-150-year-old-math-conundrum-brings-mystery/

Hope that some of you tried this and enjoyed it!

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