I took "Potpourri" for $100, and then my head started to spin

Last night's final question was: What is the maximum number of "answers" that can be read during a game of Jeopardy!?
I think a better question is this: What is the maximum number of possible "questions" (i.e., responses) during a game of Jeopardy!?


Apologies for any confusion caused by the awkward punctuation.

There must be a "One Light" pun to be made here

U2 has a concert starting in 17 minutes, and they must cross a darkened catwalk to reach the stage. All four men begin on the same side of the catwalk, and at most two can cross at a time. The band has only one torch (you know, a flashlight), and whoever is crossing the bridge must have the torch with them. Each band member walks at a different speed, and any pair crossing must walk together at the slower man's pace.
Bono takes 1 minute to cross the catwalk.
Edge takes 2 minutes to cross the catwalk.
Adam takes 5 minutes to cross.
Larry takes 10 minutes to cross.
For example: if Bono and Adam cross together, they will take five minutes to cross. If Bono comes back with the torch, he takes only one more minute.

Without throwing the torch or using Bono's superpowers (which, as we all know, include bioluminescence) or any other weird tricks, can all four band members get to the stage in time to start the show?

A Question of Adaptation

Charlie loves orchids. How can he plant ten orchids so that he has five straight rows of four orchids each?

When Garmin Fails

This week's puzzle:
Four truckers were hauling loads to four different California cities. Along the way, each trucker was delayed by an unforeseen event. Determine the name of each trucker, his cargo, his destination, and the event that caused his delay.
Some hints to help you out:

• The trucker headed for San Francisco was delayed by the car accident.
• Dave's destination was not Los Angeles.
• The town festival delayed the trucker hauling cashews.
• Ron did not go to San Francisco.
• Mr. Mason was not delayed by the rockslide.
• Mr. Reinhold was delayed by a flooded bridge.
• The trucker hauling paper was not headed for San Jose.
• Dave, whose last name was not Reinhold, was hauling sporting goods.
• Mike Anderson was not delayed by the car accident.
• Paul, whose last name was not Reinhold, was traveling to San Diego.
• Mr. Simpson was hauling oranges, but was not going to Los Angeles.

We got a thing goin' on

Last night's final question:

During the lunch hour at school, five boys from Mrs. Jones's homeroom visited a nearby lunch wagon. One of the boys took a candy bar without paying for it. When the boys were questioned by the principal, they made the following statements, in order:

1. Rex: "Neither Earl nor I did it."
2. Jack: "It was either Rex or Abe."
3. Abe: "Both Rex and Jack are lying."
4. Dan: "Abe's statement is not true; one of them is lying and the other is speaking the truth."
5. Earl: "What Dan said is wrong."

When Mrs. Jones was consulted, she said, "Three of the boys are always truthful, but everything the other two say will be a lie." Assuming that Mrs. Jones is correct, who stole the candy bar?

Addtional questions:
Don't those boys have excellent grammar and speaking skills?
Where are they going to school that they have an open campus and nearby lunch trucks?
Couldn't Mrs. Jones be a bit more helpful in identifying the rascals in her class?

He should just go to Sam's Club

Tonight's final question:
A butcher goes to market. The market sells cows for $15 each, geese for $1 each, and chickens for 25 cents each. The butcher buys exactly 100 animals, and spends exactly $100. If he bought at least one cow, one goose, and one chicken, how many of each animal did he buy?

The Middle of the Film

This was last night's trivia final:
On a certain street, there are five houses in five different colors. In each house lives a person with a different nationality. Each owner drinks a certain type of beverage, smokes a certain brand of cigarette, and keeps a certain pet. No owners have the same pet, drink the same beverage, or smoke the same brand of cigarette. Also:

• The Brit lives in the red house.
• The Swede owns a dog.
• The Dane drinks tea.
• The green house is on the left and next to the white house.
• The green homeowner drinks coffee.
• The person who smokes Pall Mall raises birds.
• The owner of the yellow house smokes Dunhill.
• The man living in the center house drinks milk.
• The Norwegian lives in the first house.
• The man who smokes Blends lives next to the cat owner.
• The man who keeps the horse lives next to the man who smokes Dunhill.
• The man who smokes Bluemaster drinks beer.
• The German smokes Prince.
• The Norwegian lives next to the blue house.
• The man who smokes Blends has a neighbor who drinks water.
• One man owns a fish.

The question is: Who owns the fish?

Tim Taylor Would Have Cleaned Up

Trivia league drama: due to a laptop crash, The Powers That Be have lost the first two weeks' worth of scores. I remember our score from week one, I think I know our score from week two, but we finished way behind those weeks, whereas we've won the two weeks since. What to do, what to do....
Anywho, we did finish in first again this week, by a single point. It would have been more, but someone (i.e., me) overruled the four other people at the table who were "pretty sure" they knew how many stars were in the Little Dipper, thus costing us a 5-point question. Of course, if the first two questions of each of the first three rounds hadn't been "guess the number"-type questions, this wouldn't have occurred. Having thought about it for a week or so, those questions bother me a lot more than what I consider overly specific questions;. After all, in a team of 4-6 people of a certain age, someone is bound to have seen Gone In 60 Seconds; how many people are going to be able to guess the first year that Chevrolet made the Corvette?
Our misses, plus two lucky guesses, and the final, which fits into the puzzle content that I am so woefully behind on:

1. What was the first Japanese car produced in the United States?
2. How many glasses (8 oz.) of milk does the average cow produce in her lifetime?
3. How many stars make up the Little Dipper?
4. What was the maximum horsepower of the original Porsche 911, which was produced in 1964?
5. In what year was the first Corvette produced?
Final:
What is the next number in this sequence:
2, 10, 30, 68, 130, 222, ???

Technological Advances in Balancing Problems

This problem I got from a fellow named Johnny Card:
Our collector has three bags of silver ingots. Well, two bags of silver, and one bag of pyrite, which looks like silver, but isn't. A pyrite ingot weighs one-tenth (0.1) of a gram more than a silver ingot. Our collector has finally purchased a digital scale, one which can measure weight to the tenth of a gram, but it is barely working (thanks to a recent incident involving weighing a chili cheese dog). The scale will certainly work once, but after that it might short out, so the collector would like to determine the fake bag as quickly as possible. How can he determine the bag of pyrite in just one weighing?

Edited to Add: Oops! I should mention that a single ingot weighs a whole number of grams - say, 100 grams. Answer in the comments.

More Weight!

Let's try another balancing problem:
This time, the collector has twelve coins, the fake doesn't weigh the same as the others, but he can't remember if it's heavier or lighter. Now, how many weighings does it take to determine the fake coin?
A hint: The previous problem relied simply on reducing the number of coins which might be the counterfeit. In this problem, the coins you know are genuine are just as important.

Going Old School

If I'm going to do this puzzle thing, maybe I should start with the classics. You know, the puzzles that everyone has seen before, but maybe not everyone remembers how to solve. And then I can explain the solution. Heck, I can run off three or four of those this week, and maybe I'll be inspired to come up with better material.
So here goes: A coin collector has a case containing eight Spanish Doubloons, one of which is counterfeit. The coins look and feel identical, but the replica is slightly lighter than the other seven coins. The collector challenges you to find the fake coin, using only an old-fashioned balancing scale (the kind with two plates: you put something on one plate, you put something on the other, it tells you which is heavier), in as few weighings as possible. What is the minimum number of weighings needed to determine the fake?

An Algebra Problem

My second run at puzzling is a test of your ability to expand a polynomial. Sorry for being overly math-y; I'll keep working on ones that are more, well, puzzles.
How many terms are there in the polynomial
(x-a)(x-b)...(x-z)?

Ramping Up the Content!

The other day, I put up a puzzle in a discussion of pirate economics. The response was just tepid enough that I decided to make this a new feature here at the Preschool. The first problem will be a variation on the earlier "pirates' council" problem. The original problem (which appeared in Technology Review a few months ago) has a neat solution - if you assume the other players are perfectly logical. In reality, I can't help thinking that pirate #5 would vote no if he were offered only two coins, thinking that, if he can just kill all the other pirates, he'd get twenty. The fact that he'll get fewer coins from the next two proposals is irrelevant - his greed overrides his decision. After eight years or so of playing and watching poker, I feel confident in saying there is no shortage of people who will give up a certain small win to try for a near-impossible big payoff. Anyway, here is the modified problem:

Five pirates are dividing a treasure of 100 gold coins. The pirates first draw lots to determine an order. The first pirate then submits a proposal for dividing the coins, and all of the pirates vote on the proposal. If the proposal does not receive a majority vote (a tie is not good enough), then the first pirate is killed, and 20 coins are paid to the executioner (who is not one of the pirates). The second pirate then submits a proposal to divide the remaining 80 coins. The process is repeated until a proposal is accepted, or there is only one pirate left. If a proposal maximizes a particular pirate’s share, in the sense that he gets MORE from this proposal then he'll get from ANY future proposal, that pirate votes “yes;” otherwise, he votes “no.”
For example, pirate #5 will vote “no” on any proposal which gives him fewer than 20 coins, because he can get 20 if he's the last one left. In fact, he'll vote against a proposal which gives him exactly 20 coins, because he can already get 20, plus the added bonus of (at least) one less pirate next time there's booty to be divvied up.
How should the first pirate propose to divide the coins in order to maximize his share?

If you read the first link, you'll see the solution to the original problem, which should make this one kind of easy. But I don't want to strain your brain just yet. I'll post the answer on Sunday; more and better problems are on their way, just as soon as I think of them.