Marigold Petals

You and I are both on a train heading from Moscow to St. Petersburg. The snow is heavy and the conductor announces that the steam exaust pipe is frozen and there will be a significant delay as the crew defrosts it. You and I share a table, and I sense you are growing bored as you look out the window and see nothing but snow. I nudge you on the shoulder and invite you to play a game with me. You nod. I take out a set of seven standard six sided dice, those seen in every run down casino in downtown St. Petersburg. I put the dice on the table, and start explaining the rules.

"Somewhere in northern Siberia there is a marigold flower."

You chuckle at this, and tell me that marigolds don't grow in Siberia.

I laugh playfully. "Well, apparently, at least one grows there. A traveller I knew told me so, for he saw it with his very own eyes. It is said that this Marigold is of a very peculiar breed. Its petals fall and grow by the minute. So my question is, how many petals are on the Marigold, right now?"

You raise your eyebrow and look at me as if I'm mad.

"Well, I'll tell you how to find out. Here I've seven 'magical' dice that can tell you exactly how many petals the Marigold has. But these dice are very fickle, and give very cryptic answers. The game, of course, is for you to figure out the language of these dice."

I then proceed to roll the dice, one by one.

The seven dice are now rolled. The numbers are 1 3 5 4 2 1 5. I muse for a minute, on purpose of course, close my eyes and pretend to chant some magic mantra, just for atmosphere, and say, "The dice tell me there are 16 petals on the Marigold."

You think for a second, and reach for one of the dice. You pick it up, examine it closely, and concludes that it is a very very ordinary die. You put it down. You tell me to roll it again.

I do. This time, I roll 6 4 1 5 3 1 3 "This time," I say after the little ritual, "there are 18 petals on the Marigold."

You tell me to roll again.

I do. This time, I roll 3 6 2 5 3 2 2. "12 petals around the Marigold."

Roll again!

I do! This time, I roll 1 1 3 2 3 3 6. "14 petals around the Marigold."

Once again, I roll. The numbers this time are 5 2 3 4 2 1 4. I look at my friend, and ask, "By now you should have enough information to see a pattern. Now you tell me, how many petals are there on the Marigold? I can roll again if you'd like."

Both of your brows are furrowed now, and you appear to be deep in thought. By now, our little game has attracted quite a crowd of other anxious passengers. After a long thought, you turn to the crowd for help.

I smile, enjoying immensely the pllight of my friend and the crowd. "Don't forget," I added cheerfully, "I'm a mathematician from the University of Moscow!"

Those of you in the crowd that have played this game before, please don't interfere. If you wished for me to roll the dice, or if you'd like the roll the dice yourself and ask me how many petals your roll represents, simply ask! It's a delightful riddle.