Having see the Singapore logic puzzle about 1,000 times in the last couple of days, I figured that it would be fun to try it out with my kids today. On the off chance that you’ve not seen the problem, here’s the Alex Bellos article about it:
The logic puzzle from Singapore
There are also mixed reports about where this problem came from – the story that caught on is that it was for middle school kids, but I don’t know if that’s true or not.
Anyway, the tough thing for my kids was understanding the implications of the first statement from Albert. I thought that it was worth spending as much time as required on that part because understanding the next statements is pretty much the same exercise. Here’s our talk through the first part:
With the hopefully thorough discussion of the first step, the next steps came a little quicker. In fact, at the end of this part of the discussion my older son sees the path to the end:
Finally, how does Albert now know the answer? As I said, my younger son was able to see the path to the end at the end of our last video. Here we go to the end and then talk about the general approach to solving logic puzzles like this one:
So, I definitely see the appeal of this puzzle. Although it really isn’t aimed at kids, my kids did have fun talking through it. I actually think that lots of kids would like talking through this puzzle even though it may be a little tough for them to understand it on their own. Definitely not a typical boring old school math problem!
Mike's Math Page 
Watching the videos, it still wasn’t entirely clear to me that they exactly understood the reasoning for some of the steps.
In a way, it is quite subtle as you have to alternate between three perspectives, each with different private information sets: A (knows month), B (knows day), and us (no private information). Also, almost all the mini-proofs in solving this puzzle are by contradiction instead of direct inference.
two suggestions when they do their next logic puzzle: (1) ask them to think about ways to organize the information and (2) when they reach an interim conclusion, ask them to write down their reasoning as mini-proofs. The first is a hugely useful mathematical skill/habit and often a key to significantly simplifying these problems. Writing down the mini-proofs, while it may seem like a bit bureaucratic/tedious, really helps make the proof by contradiction much easier to formulate and to understand.
Also, I wonder what you/they think about the reasoning that results in August 17?