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 How many oranges? (Posted on 2007-03-22)
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.

 See The Solution Submitted by K Sengupta Rating: 2.3333 (3 votes)

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 Some rotten here... | Comment 2 of 6 |
If Riley has AB apples, Sammy has AB+A+B apples, and Todd has that number, inverted.

Working mod 9, the total sum is congruent to 4(A+B).

Even if two of them have 99 apples, the other has at least 74, so A=7, 8, or 9.

272 mod 9= 2, so 4(A+B) can only be 56, and this allows A=7 B=7, A=8 B=6, or A=9 B=5.

But I must be missing something, because none of these works out!?

 Posted by Federico Kereki on 2007-03-22 15:19:59

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