When, recently, I did a conversion of a positive integral Celsius temperature, C = 275, to its Fahrenheit equivalent, it turned out to be F = 527, and I notice that I could have simply moved the digit at right of C, to the front, to obtain F. After some intense calculations, I failed to discover the next largest such example.

Does one exist, and if so, what is it?

Rewrite the numbers as C = 10X + Y and F= 10^Z * Y + X

Using the F-C relationship: F=(9/5)*C + 32 you get

(10^Z - 9/5)Y = 17X + 32

At first I thought Y would have to be 5 in order for the solutions to be integral, but I tried other values of Y and Z looking for integral solutions to X.

For Z = 14, Y = 8: X = 47058823529409 and

C = 470588235294098 and

F = 847058823529409

Of course Z = 14 is pushing the precision limit of Excel, so I can't certain something wasn't lost in one of the calculations.

Posted by Bob Smith on 2005-08-31 18:41:11