The mind-reader asks a man in his audience to
think of a number, multiply it by 5, add 6, multiply by 4,
add 9, multiply by 5, and state the result.
Audience chooses the number 12, calculates successively 60, 66,
264, 273, 1365, and announces the last number.
Mind-reader subtracts 165 from this result, gets 1200, knocks off the
two zeros, and tells Audience that 12 was the number he thought of.
The trick is easily seen if put in arithmetical symbols.
If the number A chooses is a, then the successive operations
yield Sa, Sa + 6, 20a + 24, 20a + 33, and 100a + 165.
When M is told this number, it is evident that he can determine
a if he subtracts 165 and divides by 100-or cancels the
last two digits, which are always zero.