Lee Sallows just sent me this — the puzzle is difficult, but the solution is stunning:
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The Egyptian Lo Shu
Another contribution from Lee Sallows:
“The smallest, oldest and most famous magic square of all is the specimen of Chinese origin known as the Lo shu. In this, the numbers from 1 to 9 are so placed that their sum taken in any row, column or diagonal is 15. This is another way of saying that the sum of any three of them lying in a straight line is 15. Less well known is the ‘Egyptian’ Lo shu (seen below) in which the same numbers are rearranged in a triangular formation that exhibits the same property.”
(From his book Geometric Magic Squares, 2013.) (Thanks, Lee.)
Counter Play 2
Lee Sallows sent this clever puzzle, a followup to one we presented in 2010:
In the square shown above, any 3 counters in a straight line sum to 15.
Puzzle: Reposition the counters (again, one to each cell) to produce a new square again showing eight collinear triplets summing to 15, but with 1 now placed in a corner square.
“Algebraic Theory of French Letters”
From Lee Sallows:
(Thanks, Lee!)
Podcast Episode 219: The Greenbrier Ghost
In 1897, shortly after Zona Shue was found dead in her West Virginia home, her mother went to the county prosecutor with a bizarre story. She said that her daughter had been murdered — and that her ghost had revealed the killer’s identity. In this week’s episode of the Futility Closet podcast we’ll tell the story of the Greenbrier Ghost, one of the strangest courtroom dramas of the 19th century.
We’ll also consider whether cats are controlling us and puzzle over a delightful oblivion.
Troubling Triangles
From Lee Sallows:
(Thanks, Lee!)
Zigzag
Sure Enough
From Lee Sallows, “A novel geometric proof that 16 is a square number.” :)
(Thanks, Lee!)
Inventory
Lee Sallows sent this self-descriptive rectangle tiling: The grid catalogs its own contents by arranging its 70 letters and 14 spaces into 14 itemizing phrases.
Bonus: The rectangle measures 7 × 12, which is commemorated by the two strips that meet in the top left-hand corner. And “The author’s signature is also incorporated.”
(Thanks, Lee!)
