You can tell about when the puzzle will end by where on the page it says "Puzzle will end: {Day of the week} most likely".
That is more or less (if not always) the right date give or take 24 hours.
The new puzzle is always updated a few minutes after the "New Features" page is updated with the new event "A new Lenny Conundrum has begun, the answer to the last one was
{answer}, {Number} of people got the correct answer, earning them {Number} NP each." (That's usually how they read, more or less). New features I believe is updated about 5PM NST. Be sure to be carefull if you see a new Lenny went up about the same time New Features was updated. I recently accidentally went to the new riddle before it was updated and found myself with a solution for last riddle from the week before. Two riddles in one day.
what fun!
Anyway, I've solved Lenny Conundrum 3 times now, and I hope that I solved this weeks correctly and as one of the first 250. Only got a trophie for one win though (my first one). The first one I did was really fun, it had to do with meowclope standing in the middle a room. It had am eyesite range of so many degrees, and the question was what percent of the room could it view.
Lots of trig in that one. The prize to it was a Plushie Meowclopes (Not a Meowclops Plushie, that's a toy, I won a painted petpet). That was the first that it was released, and it was emidiatly retired. So only 500 are in exsistance in Neopia today.
Sorry... that was a bit of bragging at the end... I'll stop now... >_>