Well, I’m a little late with this week’s installment. This is properly last week’s installment. But it has been crazy around here! Seriously! Again, I have to link to the most appropriate song for the end of every semester as a math professor–The Final Countdown. Thank you Europe. If you, you in all your big-haired glory, only knew the terrible unrealistic air guitar that has been played to your song by the mathematically stressed, well, I think you would be a little surprised. And hopefully proud. The song is most appropriate in combinatorial situations, but I try to fit it in to my life ever’ damn semester.
I will be getting back to blogging about things other than puzzles in a couple of weeks, after Math Mostly runs its last episode this Friday. Only one more puzzle, and no waiting for an answer! It is sure to be a very special episode of Math Mostly, filled with tears and maybe a montage of the best moments of the semester. Plus I will announce the winner of the big semester contest. I think we’ve got it figured out, unless there are some last minute answers from one close contender… So it’ll be great! However, I was just trying to share a little news about something mathy other than the show. My recent paper, with Rachel Pries and Bob Guralnick, was just accepted to the Journal of Algebra! That’s awesome! I am so excited. This is likely to be the last paper directly out of my thesis projects, so I’d better get working on some new math. Or work harder on what I’ve started anyway. So watch out, math, I’m coming to get you.
So now the puzzle! This week’s puzzle involves my co-host Jed and his maple syrup farming uncle. It was a bad year for maple syrup, I hear, and the farmers have my sympathy. Jed visited his uncle a few weeks ago and found him with a dilemma. The uncle some containers on hand that he usually used to give his maple syrup gifts to the family. There are two sizes–one that holds exactly 4 cups and one that holds exactly 6 cups. They are perfect cylinders–circular, right cylinders. And no, I’m not going to tell you the diameters or heights, because you don’t need that information to solve the problem. Which is this: Jed’s uncle has calculated that since it was such a bad year, he can only afford to give gifts of 1 cup of syrup to each of his family members. Fine, but he doesn’t have any one cup containers. So he wants to use the old ones, but containing only exactly one cup of syrup. Jed shows up for a visit, and his uncle needs to measure out exactly one cup of syrup for his gift. How can he do it, using only the existing 4 and 6 cup containers and no other measuring devices?
If you know the answer, send it to email@example.com! And tune in this Friday to hear the answer, as well as find out who won the big prize. 2:30-3 pm on WESU 88.1 FM Middletown, or wesufm.org anywhere with the internet.
Oh yes, and what about last week’s puzzle? That was the one involving the hats. On Pi day. Okay, so the situation is that all of the people must be wearing red hats. Why? There must be at least two red hats because everybody has his hand raised. However, what if there were only two hats? Say A and B are wearing red hats, and C is wearing a blue hat. Then, A would look at B and see that B’s hand was raised, and think–B must see a red hat. However, the only hats that B can see are A’s hat and C’s hat, which is blue. So A would immediately know that he must have a red hat, and would have stood up right away to claim the prize. B would have been in the same situation, so they would have had to fight for the tart. Since nobody acted right away, it must be that nobody is in a position to make such an immediate action–there must in fact be 3 red hats. So the first person who sees that the lack of action is actually a piece of information will stand up and declare her red-hattedness. Congratulations to Anwar, the winner of the puzzle. He won an amazing T-shirt–I will definitely post the design for you soon.