Let us consider a sequence whose first term is 1.2 - and, the numbers appearing respectively to the right and the left of the decimal point of a given term are swapped and this number is added to a given term to obtain the next term.

For example, if a term is 46.78 then the next term will be 46.78+ 78.46 = 125.24.

For some of the terms in the sequence, the numbers appearing before the decimal point and the numbers appearing after the decimal point are congruent. Considering the first 30 terms, how many terms do have this property?

Note: Terms like 792.792 are deemed to have the desired property. However terms like 3870.387 do not possess this property as 3870 is not equal to 387.

(In reply to re: The easy way is turning out to be hard by Jer)

I agree. I actually used mathematica to manually compute the excel entries after 26, to obtain 13 solutions, but I notice having seen Charlie's answer that there is still an issue with line 24.

 Excel can be very annoying at times.

Edited on November 16, 2011, 10:44 pm

Posted by broll on 2011-11-16 22:40:29