Mark Dominus poses this question:
Suppose S is a multiset whose elements are among the numbers 1, 2, ... 9. Say that S is "good" if there is some arithmetic expression involving only +, -, ×, and ÷, that uses all of the elements of S and has a value of 24. For example, S = {1, 1, 2, 8} is good because 1×8×(1+2) = 24, but S = {1,1,2,5} is not good. (Proof omitted.) It's easy to show that every sufficiently large S is good. What's the maximal example of a bad S?
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