Solution to Andy Naughton's magic trick

February 3, 2006 -- This is the solution to Andy Naughton's trick at Congratulations for a well conceived one! (And thanks to Terri for bringing my attention to it.)


You choose a number AB (where A is the first digit and B the second digit). The result of your calculation will be:
(10A +B) - (A + B) = 9A.
This means that, whatever B you choose, your answer can only be one of the following 9 numbers (given A between 1 and 9): 9, 18, 27, 36, 45, 54, 63, 72, 81. If you check the table of numbers and symbols on the magic page, you can observe that the symbols change at each round in order to confuse you, but in any given round, the symbol is always the same for these 9 numbers. Your calculation necessarily gives a result associated with the unique symbol assigned to the 9 possible solutions.


"Mathematics is a language."
-- J. Willard Gibbs


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