Due March 7

This problem can be solved by trial and error. We consider this to be a hard problem, worth 25 points. Send answers and questions to mathstat@uoguelph.ca

We want to test a group of 7 food additives to see if any pairs of chemicals have bad cross-reactions that produce toxins. Since the test for toxins is expensive we mix the food additives in groups of three before sending them to the lab so that each test checks for toxins in the three pairs (for additives A, B, C the pairs in the mixed triple would be AB AC and BC, for example). Since triple cross-reactions are very rare, this is a sensible cost saving strategy. Find a collection of triples of additives A, B, C, D, E, F ,G so that (i) every pair is in a triple and (ii) the number of triples is a small as possible. Since there are 21 pairs you should need a good deal less than 21 triples.

Send your answer to mathstat@uoguelph.ca

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