Pi Day Hat Game Three Way Stand Off!
This week’s puzzle is about a Pi party gone horribly wrong. Okay, not really horribly, but pies were ruined, and the remaining desert became the prize in a hair-raising battle of logical thought. It all starts with a Pi Day (3/14, that is) dinner party at my friend Hannah’s house. She is a compulsive knitter, by the way, and is constantly knitting stocking caps. She made a bunch of amazing pi-themed dishes and invited me and two other friends (call them Alice and Charlie) over for dinner. We were all feeling happy and math-tastic after dinner when Hannah went into the kitchen to get desert. Hannah had made the most beautiful little rhubarb-pi tarts for desert. Having had Hannah’s baking before, Alice, Charlie and I were really excited about these tarts. So we were dismayed when we heard a clattering sound and a splat from the kitchen, followed by Hannah’s dismayed cry of “Oh ****! I dropped the tarts!”
Three of the tarts were destroyed! On the kitchen floor, face down, currently being gobbled by Hannah’s dog. The final tart was shaken but unharmed. Hannah came in from the kitchen, bearing said tart, and said, “This one tart will never divide four ways. That’s like one bite each. No way. We’ll have to play a game to decide who gets it.”
Hannah decided that just the three guests would compete–she would make herself some tarts another time. So Alice, Charlie and I looked at each other with growing coldness. Our eyes shifted back and forth, just like we were the Good, the Bad, and the Ugly. This was serious. Hannah disappeared into her knitting room and came back with a big box of hats. Strangely, they were all red or blue, and there were a ton of each color. She told us all to hold still, and then came up behind us in turn and put a hat on each of our heads. We couldn’t see our own hats, but we could each see the other people’s hats. Hannah explained the rules.
“Each of you is wearing either a blue hat or a red hat. When I say go, raise your hand if you see a red hat. When you figure out the color of your own hat, stand up. The first person to figure out the color of her hat wins. Okay, now GO!”
We all raised our hands. Then nothing happened for a while. We stared at each other, and stared some more, hands in the air. Things were getting tense when suddenly, I realized that I did know my hat color! I hadn’t known at first but all that waiting had told me something. I jumped into the air, correctly announced the color, and snatched my delicious prize.
The puzzle this week is–what color was my hat, and how did I know?
Send your answer to firstname.lastname@example.org! Best answer wins a math mostly/somewhat science T-shirt. The shirts are on order and are coming really soon! See what I’ve been doing when I should be proving theorems. Also, we’ve got another contest going, where the awesome mystery prize goes to whoever sends in the most correct puzzle answers over the whole semester. Only about 4 weeks to go, so keep them coming.
Ah yes, and now for last week’s puzzle. I love the tournament puzzle. The question–how many games need to be played in a single-elimination, March madness style tournament with 10,041 teams? By single elimination I mean that a team is eliminated after one loss, and one winner is wanted at the end of the tournament. The answer is–10,040 games. The way to see this really quickly is to notice that each game has one loser. We want one winner, so the other 10,040 people have to lose. Thus we need 10,040 losers, so 10,040 games. Congratulations to last week’s winner, Hanako!