So I was walking through the game section today, which is typically my strong point. I came across this game involving the dancers, and I have no idea for the life of me how to solve it. There were no deductions I could make to help me answer the questions, so I'm guessing there was something I'm missing. If there's someone who figured this one out, I'd appreciate a step in the right direction (or a full on explanation as this one left me clueless). Thanks so much.

Combining the second and third rules, we know that T will partner with L or M in the first dance. Working out the possibilities with K and L/M (applying the third rule) reveals that there are only four unique assignments that meet all the conditions.

This game is all about getting off to a good start with a good diagram. I use a grid. I have three columns for the three dances. I have three rows - one for each boy. Then, I just put his dance partner in the box that matches the column and row.

Using the initial restrictions, you should first figure out that K must dance with T or R in Dance 3. From there you should see that K must be with S or T in Dance 2. That is all you need from the original restrictions. However, each time you get a local restriction and add it to this grid, as soon as you start applying the original restrictions to it, the grid is completed fairly quickly (as far as is necessary for the question) and then the questions are no-brainers.

Oh, wow, ok, the way I had read it was that there were 3 dances, and 1 pair of children was going to perform each dance, which meant that only two would go on at a time, so I set up a list instead of matching, not that all 6 would be dancing at once. That was the killer, I guess nothing said 'grid' to me on that one.

Thanks for all the help.