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Pair Sums

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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Weekly Problem 16 - 2012

Weekly Problem 16 - 2012

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Weekly Problem 47 - 2013

Weekly Problem 47 - 2013

Weights

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

The largest total you can make is $20$ ($2A + 2C$).

The smallest total you can make is $-60$ ($2B + 2D$).

There are some totals that are easier to produce than others (perhaps those that require just one or two weights), so it may be a good idea to start with those and then build on them with a few extra weights.