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Sam Loyd's unsolved patterns
The eighth book of Tan - 700 Tangrams by Sam Loyd with an introduction and solutions by Peter Van Note Dover publications Inc., New York 1968
The book by Loyd is one of the most famous source on Tangram and it is a sort of spoof of tangram history, The Eighth Book Of Tan convincing many people that the game was invented 4,000 years ago by a god named Tan. In the introduction of 1968 Dover edition, Van Note says: ' ... a few (patterns) would seem not to be true tangrams.' We report them here.
page 15 SILHOUETTES
The fourth head from left on the second line is not a proper tangram.
page 17 KITTENS AND BUNNIES
Two kittens around a milk bowl. The bowl cannot be a proper tangram, being a convex figure not included in the list of the thirteen allowed tangram convex silhouettes.
page 19 ANIMAL FIGURES
The goat silhouette, the third from right in the second line, in the illustrations for the rhyme of Noah's ark:
'The animals walked in eight by eight, Butted on by a goat, 'cause he thought they were late.'
Van Note reported the pattern as unsolved, but it is a proper tangram.
page 25 PARADOXICAL FALLACIES
'With the figures of the three cabinet organs we reach that borderland of mystery in the black art which can be only solved mathematically. ... yet the last one shows a folding lid which calls for an extra piece! Indeed, the third one only is a true tangram.

'The seventh and eighth figures represent the mysterious square, built with seven pieces: then with a corner clipped off, and still the same seven pieces employed.'
The clipped square cannot be a proper tangram, being a convex figure not included in the list of the thirteen allowed tangram convex silhouettes.
In our opinion, the solution to Loyd's paradox is in the first figure, where the square and the clipped square are obtained using just ONE set of tangram. The small spike in the clipped square is due to the difference between 2xSqrt(2) and 3, the very same difference which Loyd neglects in his explicit solutions in the comparison between the pyramid and the truncated pyramid. posted 3_12_2008s0
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Numbered giclée The tale of 2 bunnies by F.C.Keen The Number 5 Triangle Puzzle Trailer on F.C.Keen's book Sam Loyd's unsolved patterns TANBRICK - Match tangram pieces as toy bricks





The eighth book of tan






















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