1989 AJHSME Problems/Problem 18
Contents
[hide]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
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
See Also
1989 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |