olymmath

AIME 2007a Problem 5

  • Paper
  • Answer

The formula for converting a Fahrenheit temperature FF to the corresponding Celsius temperature CC is C=59(F−32).C = \frac{5}{9}(F-32). 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?

Dataset text AIME 1983 to 2026. Quoted with source.

Show the answer

539

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.

Add a solution

Locator aime/2007a/p5 · Tag YXZW7QVPJM · Edit this page on GitHub · Keys: j next, k previous