Everything you need to solve this riddle can be found in the numbers you see here. Be apprised: The mathematically inclined tend to struggle with this puzzle.
I'm on the road this week, so this week's puzzle is short and sweet – but still quite challenging, in my opinion. It's another classic, so if you know the answer try not to spoil it in the comments.
We'll be back next week with the solution – and a new puzzle! Got a great brainteaser, original or otherwise, that you'd like to see featured? E-mail me with your recommendations. (Be sure to include "Sunday Puzzle" in the subject line.)
Last week, I asked you to untangle the lines of descent of an unusual family tree.
This is the kind of puzzle that can really benefit from diagramming. I recommended you try using pencil and paper (which I needed, personally, to solve the riddle). Many of you submitted drawings and images of your puzzling process ( well done!), but the first to send me a solved family tree was Edward Kim. His diagram and accompanying explanation are as clear as any solution I could hope to provide, so I've embedded them below:
"This scenario is somewhat similar to a famous Indian riddle, which is at least 1,000 years old, since it occurs at the climax of the Baital Pachisi," writes Phil Winkelman,who originally suggested this puzzle via our Sunday Puzzle tips line. "However, in this tale, a man and his son meet a woman and her daughter – the man marries the daughter and the woman the son. This scenario reached its cultural apogee (or nadir) in 'I'm My Own Grandpa'." (Some of you noted the similarities between this puzzle and "I'm My Own Grandpa" in the comments.)
Many of you inquired about incorporating step-relations and in-laws into the solution to Lichtenberg's riddle. Lichtenberg himself proposed such a scenario as a preliminary solution to the riddle in The Waste Books (translated by R. J. Hollingdale). This excerpt has been annotated by Winkelman, whose comments appear in brackets (please excuse my horrendous penmanship in the diagram below; I am writing this from a frigid campsite in northern California, and I forgot my gloves):
Two old men [M1, M2] each of whom has a grown-up son [M3, M4] each of whom has an unmarried daughter [F1, F2] marry two young girls who are sisters [F3, F4]. After the wedding, however, the two old men are ill and die before the marriages are consummated. After their deaths the two young men marry their stepmothers: these six last [shaded boxes] are those who lie buried here. For here two sisters are also lying with their two brothers[-in-law], because every woman calls her sister's husband her brother.
"Not only is there a fudge-factor with the stipulated 'brothers' actually panning out as brothers-in-law," writes Winkelman, but Lichtenberg's preliminary solution requires that daughters, mothers, and grandmothers be regarded as step-relations. "The correct solution," he notes, and as we see in Edward's solution above, "does not require these feints."
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