Lewis Carroll's Number Trick

In Lewis Carroll's The Hunting of the Snark, the Butcher is trying to explain to the Beaver why 2 + 1 = 3.

"Taking Three as the subject to reason about --
A convenient number to state --
We add Seven, and Ten, and then multiply out
By One Thousand diminshed by Eight.

The result we proceed to divide, you see,
by Nine Hundred and Ninety and Two:
Then subtract Seventeen, and the answer must be
Exactly and perfectly true."

The arithmetic described in this verse is straightforward.   In trying to explain to the Beaver why 2 + 1 = 3, the Butcher starts with 3, adds 7 and 10, and multiplies by 1000 - 8 (which is 992).   He then divides by 992 and subtracts 17, taking him back to where he started -- namely 3:



In fact, any number other than 3 would have done equally well -- the Butcher must always end with the number he started with.

Send any comments or questions to: David Pleacher