A puzzle by Polish mathematician Paul Vaderlind:
If a blacksmith requires five minutes to put on a horseshoe, show how can 8 blacksmiths shoe 10 horses in less than half an hour?
The catch: A horse can stand on three legs, but not on two.
Label the horses a through j and the blacksmiths 1 through 8.
Each row below represents one 5-minute round, assigning one horse with one blacksmith.
Start initially with this staggered arrangement:
a1 b2 c3 d4 e5 f6 g7 h8
b1 c2 d3 e4 f5 g6 h7 i8
c1 d2 e3 f4 g5 h6 i7 j8
d1 e2 f3 g4 h5 i6 j7 a8
e1 f2 g3 h4 i5 j6 a7 b8
Here horses e, f, g and h have 5 assignments each but of course need only 4, while horses a, b, c and j have only 3 each. Reassign as follows:
a1 b2 c3 d4 e5 f6 g7 j8
b1 c2 d3 e4 f5 a6 h7 i8
c1 d2 e3 b4 g5 h6 i7 j8
d1 c2 f3 g4 h5 i6 j7 a8
e1 f2 g3 h4 i5 j6 a7 b8
Voila!
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Posted by Charlie
on 2015-08-13 09:26:03 |
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