Problem 17 · 2009 Math Kangaroo
Hard
Number Theory
casework
In the equation E×I×G×H×TF×O×U×R = T×W×O each letter represents a certain digit (the same letter represents the same digit each time). How many different values can the expression T·H·R·E·E have?
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Answer: A — 1
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Hint 1 of 2
Ten different letters stand for the ten different digits - so one of them must be 0.
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Hint 2 of 2
Ask what the product T x H x R x E x E becomes once a 0 is in play.
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Approach: spot the forced zero
- The ten distinct letters use every digit 0-9, so exactly one letter is 0.
- A 0 sits among T, H, R, E in any valid arrangement, making the product T x H x R x E x E equal to 0.
- So the expression can take only 1 value (it is always 0).
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