Friday, October 22, 2010

PUZZLE: Longfellow's Bees

Henry Wadsworth Longfellow introduced several Sanskrit puzzles to American audiences as part of his novel, Kavanagh. Among them was this one:

"One-fifth of a hive of bees flew to the Kadamba flower; one-third flew to the Silandhara; three times the difference of these two numbers flew to an arbor; and one bee continued flying about, attracted on each side by the fragrant Ketaki and the Malati. What was the number of the bees?"


Chris Mildebrandt said...

h is the total number of bees in the hive:

h = (1/5)h + (1/3)h + 3h(1/3 - 1/5) + 1
h - (1/5)h - (1/3)h - 3h(1/3 - 1/5) = 1
h(1 - 1/5 - 1/3 - 1 + 3/5) = 1
h(2/5 - 1/3) = 1
h(6/15 - 5/15) = 1
h(1/15) = 1
h = 15

Thomas L. McDonald said...

Wow, that was fast!

Chris Mildebrandt said...

I'm happy to goof off for a bit on a Friday.

Chapin said...

Damn you and your algebraic ways!

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