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I have a balance for weighing things, and a set of kilogram weights, 1kg through 9kg weights. So I can easily weigh things up to 45kg through some combination of the weights.
However, for quiz-related reasons too complex to go into, I need to take my balance and weights to a new location to weigh objects up to 20kg in weight (the objects are conveniently always a whole number of kilos in weight.).
But the excess baggage charges are astronomical for this journey. If I took all my weights, I'd be ruined. What's the minimum (in total weight, giving the individual weights) I need to take with me to be able to measure the weight of any object that's a whole number of kilos between 1 and 20 inclusive?
Hint: The total of the weights must be at least 20kg. If you find more than one minimum total weight solution, choose the one with fewer weights.
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