1989 AJHSME Problems/Problem 18
Problem
Many calculators have a reciprocal key that replaces the current number displayed with its reciprocal. For example, if the display is and the key is depressed, then the display becomes . If is currently displayed, what is the fewest number of times you must depress the key so the display again reads ?
Solution
Let . We have Thus, we need to iterate the key pressing twice to get the display back to the original .
Solution 2 (simpler, no use of functions)
In terms of mathematics, a number will always be changed back to its original number if you flip, or "reciprocal" it, twice. Therefore, no matter what number it will display, the answer will always be
~DuoDuoling0
See Also
1989 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
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