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Part of 2011 Canadian Mathematical Olympiad Qualification Repechage

Problems(1)

What are the five numbers? - [Canadian Repêchage 2011]

Source:

Brennan chooses a set

A = \{a, b,c, d, e \}

of five real numbers with

a \leq b \leq c \leq d \leq e.

Delaney determines the subsets of

A

containing three numbers and adds up the numbers in these subsets. She obtains the sums

0, 3; 4, 8; 9, 10, 11, 12, 14, 19.

What are the five numbers in Brennan's set?

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