Determine all possible values of a positive integer x satisfying:

x degrees Fahrenheit = sod(x) degrees Celsius, where sod(x) denotes the sum of the digits in the base ten expansion of x.

Prove that there are no others.

Note: To convert from degrees Fahrenheit to Celsius, subtract 32 then multiply by 5/9. To convert the other way, simply do the opposite (multiply by 9/5 and add 32).

If the number is AB in fahrenheit then

( B +10A-32)*5/9 = A+B or 41A-4B=160

 Only integer solution for different values of A is A=4, B=1

Posted by Salil on 2013-04-08 04:38:11