Problem of the Week

PROBLEM 227

The following problem is from the Illinois State MAA 2004 Student Mathematics Competition.

Pat selected five different integers and formed the sums of pairs, then wrote down the ten results, some of which were wrong, as: 2,4,5,7,7,8,10,11,12,13.  Chris, who was checking Pat's work, told Pat that the first three and the last three sums were correct, but that some of the others were wrong.  What are the five integers? 

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ã2005 Alberto L. Delgado