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The 1089 trick

numbersdigitsmagic-trickalgebra

Choose any three-digit number whose first and last digits differ by at least 2, for example 742. Reverse it (247) and subtract the smaller from the larger (742 minus 247 = 495). Now reverse that result (594) and add the two (495 + 594).

What do you get, and why does everyone get the same answer no matter which number they start with? What goes wrong if the first and last digits differ by less than 2?

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Write the number as 100a + 10b + c. The middle digit cancels in the subtraction. Then look carefully at the borrowing.

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The Substitution That Collapses the AlgebraFunctional EquationsNested Radicals and Infinite FractionsSolving Linear Recurrences With Characteristic RootsTelescoping Sums and Products

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