The problem seems to be limited to pennies, nickels, dimes and quarters; if so there are two solutions (and if not I think the problem is even more poorly framed, if possible).
There are 3 given that constraint.
(0,0,1,4,0,0)=110 (0,9,1,0,0,0)=55
(0,0,1,4,0,0)=110 (5,0,5,0,0,0)=55
(1,0,1,3,0,0)=86 (8,0,1,1,0,0)=43
The kids given this problem aren't learning combinatorics, really, ... I'd be thrilled if this problem had been presented correctly in the context of learning some combinatorics.
There in lies the difference between the GT world and non GT world. I can see teaching this in many ways - whole numbers, graphs, tiles, harmonics, learning to program, etc. Your average teacher sees pennies, nickels, dimes, and quarters. LOL.
A good math teacher could spend a month teaching just this problem to 2d graders who are 2+ SD on math ability.
