Three friends Riley, Sammy and Todd have a certain number of oranges in their possession.

It is known that:

(1) The number of oranges possessed by each of the three friends are two digit positive integers.

(2) The number of oranges possessed by Sammy is obtained by adding the two digits of the number of oranges possessed by Riley and summing the result with the original number of oranges in Riley's possession.

(3) The number of oranges possessed by Todd is obtained by reversing the digits corresponding to the number of oranges in Sammy's possession.

(4) The total number of oranges possessed by the three friends is 272.

Determine analytically the number of oranges possessed by each of the three friends.

Let (R,S,T) = the number of oranges held by Riley, Sammy, Todd respectively.

If S = 10k + j, by (3) T = 10j + k so S + T = 0 mod11 and then by (4) R = 8 mod11.

Since S + T < 200, R = 74,85 or 96.

R = 74 implies T>100 and R = 96 implies S>100.

(R,S,T) = (85,98,89) satisfies all the problem's conditions.

Posted by xdog on 2007-03-22 15:14:09