I'd heard about the dice-based brain teaser Petals Around the Rose but didn't read the details until tonight when I followed Bob Congdon's link to this page.
At the outset of reading the latter, I decided I would try to work it out myself and not cheat by Googling the answer. I had a couple of hypotheses but none of them worked past one or two of the sample rolls given.
By the end of the page, I hadn't worked it out. Bob Congdon had suggested "the less you think about it the easier it is to solve" so I stopped thinking about it all together and started getting ready for bed.
Then it all of a sudden hit me! I rushed back to the computer and tested my hypothesis. I was right every time!
Go read the article for yourself. Even if you don't get it right away, stop thinking and let it come to you. Nothing beats working it out yourself.