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 Three subsets (Posted on 2014-08-15)
You are requested to create 3 disjoint sets such that:
1. Their union is a set of 10 digits (i.e. integers from 0 to 9 inclusive).
2. The average value of the members of set A is 3.5.
3. The number of members in B is less than the number of members in C.

How many distinct solutions are there?

Rem: No empty sets.

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 re: computer solution | Comment 2 of 13 |
(In reply to computer solution by Charlie)

Huh?  Are we doing the same problem?

There are three sets, A and B and C.  B has smaller cardinality than C, not A.  A can have 2 or 4 or 6 elements.  The number of solutions is much, much bigger than 9.  Don't have time to count now, but here's one:

A = {0,7}  B = {1,2,3} C = {4,5,6,8,9}

Edited on August 15, 2014, 3:14 pm
 Posted by Steve Herman on 2014-08-15 15:12:38

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