Difference between revisions of "2007 AIME I Problems/Problem 5"
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== Solution == | == Solution == | ||
| − | Examine <math>F - 32</math> modulo 9. | + | Examine <math>F - 32</math> modulo 9. |
| + | == Solution 2 == | ||
| + | Hint. Consider the identity <math>Round(ax)=Round(xRound(a/Round(ax))</math> its something like that... | ||
== See also == | == See also == | ||
Revision as of 22:55, 14 March 2007
Contents
Problem
The formula for converting a Fahrenheit temperature 
to the corresponding Celsius temperature 
is 
An integer Fahrenheit temperature is converted to Celsius, rounded to the nearest integer, converted back to Fahrenheit, and again rounded to the nearest integer.
For how many integer Fahrenheit temperatures between 32 and 1000 inclusive does the original temperature equal the final temperature?
Solution
Examine 
modulo 9.
Solution 2
Hint. Consider the identity 
its something like that...
See also
| 2007 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
