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Here's one of my favourite questions that I've ever solved -- it lasted for weeks of a few minutes a day! It's actually a modified (by me!) version of a very well known type of question, the "find the counterfeit coin in x weighings with a balance scale" question. I found it in a puzzle...

If anyone went to NMSS or ISS, it'd be cool if you let me know, I'd like to know who you are when I'm reading your posts (especially re HSC marks and UAIs), since so far I've only seen one person I know, and they only posted once! Or for that matter, anyone going to this year's NMSS tell me...