Car talk plaza puzzler revisited

[Sabertooth]

Don't Do It, Frank!
RAY: An off-duty policeman is working as a night watchman in an office building. He's doing his rounds and he comes upon a closed door. Behind the door he hears voices; people are talking and an argument seems to be taking place. He hears someone say, "No, Frank, no; don't do it, you'll regret it." Bang! Bang! Bang!

The night watchman bursts through the door; what does he see? A dead man on the floor. And the proverbial what? Smoking gun.

And in the room, are three living people; a minister, a doctor, and a plumber. He walks over to the minister and says, "You're under arrest. You have the right to remain silent."

How does he know that it was the minister that pulled the trigger?

Answer:
RAY: Here's the answer. Only one of them could have been named Frank, because the other two, the plumber and the doctor, were women.

 

[Sabertooth]

Shipwrecked Saga
RAY: This is the first in the rising floodwaters series. A family of four and their dog get trapped on an island when rising floodwaters tear out the bridge they used just a few hours before. Frantically they search for some means of crossing back to the mainland and finally when they've just about given up hope, the son says, "I found a small boat and oars." They gather around but their joy is short-lived because the manufacturer's instructions -- printed on the back of the boat -- say that the boat can carry only 180 pounds. Thank God Grandma's not here. It's just Mom, Dad, the two kids, and the dog. And the dog is the only one of them who can swim.

Well, the father weighs 170. The mother says she weighs 130. The son is 90 pounds. And the daughter is 80. The dog weighs 15 pounds. Everyone can row except the dog, who can swim. And the question is: is there any way the family can be saved? And if so, what are the fewest number of crossings to save everyone?

 

[returntosender]

Thanks Saber

 

[Sabertooth]

Shipwrecked Saga
RAY: This is the first in the rising floodwaters series. A family of four and their dog get trapped on an island when rising floodwaters tear out the bridge they used just a few hours before. Frantically they search for some means of crossing back to the mainland and finally when they've just about given up hope, the son says, "I found a small boat and oars." They gather around but their joy is short-lived because the manufacturer's instructions -- printed on the back of the boat -- say that the boat can carry only 180 pounds. Thank God Grandma's not here. It's just Mom, Dad, the two kids, and the dog. And the dog is the only one of them who can swim.

Well, the father weighs 170. The mother says she weighs 130. The son is 90 pounds. And the daughter is 80. The dog weighs 15 pounds. Everyone can row except the dog, who can swim. And the question is: is there any way the family can be saved? And if so, what are the fewest number of crossings to save everyone?

Answer:
RAY: Now, the fact that the dog can swim is a red herring. Because the dog doesn't have to swim at all. Here's how it's done. The boy and the girl row over to the mainland.

And that's 170 pounds. One of them comes back. Doesn't matter which one. On the next trip the mother and the dog row to safety.

So now we got one of the kids over there, the mother and the dog. But now the other kid comes back. So the only two that have reached safety so far are the mother and the dog. The boy and the girl row over again. One of them comes back. The father rows over. The other kid comes back to the island and now the two kids row to safety together. And then when they get there, they look for the car.

How many trips was that? It's nine crossings.

 

[Sabertooth]

Frank's Party of Five
RAY: My neighbor Frank says to me one day, he says I have five children. I say I know that. He says half of them are boys. I said I'll get right back to you. Can you explain that?

 

[Sabertooth]

Spoiler: My Guess(es)

1. He has three boys & two girls. That satisfies the minimum of 2.5 boys.
2. He has two boys & two girls and his wife is pregnant with a child of undetermined gender.

 

[Sabertooth]

Frank's Party of Five
RAY: My neighbor Frank says to me one day, he says I have five children. I say I know that. He says half of them are boys. I said I'll get right back to you. Can you explain that?

Answer:
RAY: Now people immediately start thinking about dogs, cats, canaries, and the like. They figured somehow or other he's miscounting.

Five children. I mean how can you have -- how can half -- how can you have five and then half, right? Does he have half a boy?

Well, he does. And it would be correct to say that ten percent of them are boys. Sixty percent of them are boys, and a hundred percent of them are boys.

Therefore...

They're all boys. Half of them are boys. Are they not?

 

[Sabertooth]

Pinewood Derby Debacle
RAY: This is a quasi-automotive puzzler, sent in by John Whittier. He writes;

"This is the season for Cub Scouts all over the country to hold their Pinewood Derby Races. My two sons built their cars and wanted to compete against each other at home prior to the real race. I built a simple racetrack using materials I had on hand.

However, I only had materials to build a one-lane track. I had planned to run the cars individually and use a stopwatch to time each car. So, son A would put his car at the top and let it go. I'd start the watch, and when it got across the finish line, I'd check the time.

But when we attempted to hold races I discovered that the cars traversed my very short track in such a short time that I could not start and stop the watch fast enough to accurately measure the times such that we could really determine which car was faster.

My younger son, who was eight years old, came up with a solution. Remember, all we had were the two cars, the short test track, the stopwatch, and the three of us.

What solution did he come up with?"

 

[Sabertooth]

Pinewood Derby Debacle
RAY: This is a quasi-automotive puzzler, sent in by John Whittier. He writes;

"This is the season for Cub Scouts all over the country to hold their Pinewood Derby Races. My two sons built their cars and wanted to compete against each other at home prior to the real race. I built a simple racetrack using materials I had on hand.

However, I only had materials to build a one-lane track. I had planned to run the cars individually and use a stopwatch to time each car. So, son A would put his car at the top and let it go. I'd start the watch, and when it got across the finish line, I'd check the time.

But when we attempted to hold races I discovered that the cars traversed my very short track in such a short time that I could not start and stop the watch fast enough to accurately measure the times such that we could really determine which car was faster.

My younger son, who was eight years old, came up with a solution. Remember, all we had were the two cars, the short test track, the stopwatch, and the three of us.

What solution did he come up with?"

Answer:
RAY: He very simply said, "Let's put both cars on the track, one behind the other."

If the front car, that is the car closest to the finish line is faster when we release the two cars simultaneously, of course, that one will pull away from the other one, and it will be the faster car.

Otherwise, the other one will push it over the finish line.

Once you've done that first heat, you're going to reverse the cars' position and see if in fact that no gap opens and then the rear car, which had been the front car, will be the faster car.

 

[Sabertooth]

1000 $1 Bills and 10 Envelopes
RAY: I'm going to give you a thousand $1 bills. You come up with 10 envelopes.

Here's your assignment: Figure out a way to configure those 10 envelopes, that is, to put various numbers of dollar bills in those 10 envelopes, so that no matter what amount of money I ask you for, you can hand me some combination of envelopes and always be assured of giving me the correct amount of cash.

If I say, "Give me $637," you can say, "Oh, that will be envelope number one, envelope number six, and envelope number two."

Got it?

 

[Sabertooth]

Spoiler: My answer

#1: $1
#2: $2
#3: $4
#4: $8
#5: $16
#6: $32
#7: $64
#8: $128
#9: $256
#10: $489

$637 = #10 + #8 + #5 + #3

As a programmer, I should have seen it sooner...
This solution (with $512 in #10) will work all of the way to $1023. 1 kilobyte in computer-speak is actually 1024 bytes.

 

[Sabertooth]

1000 $1 Bills and 10 Envelopes
RAY: I'm going to give you a thousand $1 bills. You come up with 10 envelopes.

Here's your assignment: Figure out a way to configure those 10 envelopes, that is, to put various numbers of dollar bills in those 10 envelopes, so that no matter what amount of money I ask you for, you can hand me some combination of envelopes and always be assured of giving me the correct amount of cash.

If I say, "Give me $637," you can say, "Oh, that will be envelope number one, envelope number six, and envelope number two."

Got it?

Answer:
RAY: I gave Tommy a thousand $1 bills, and his assignment was, first, come up with 10 envelopes, and once he did that he had to figure out a way to put various numbers of dollar bills in those 10 envelopes so that no matter what amount of money I asked him for, he could hand me some combination of envelopes and always be sure of giving me the exact right amount. The question is: How did he do it?

That's the question, you thought the question was, “What was going on in your mind that you gave me 1,000 $1 bills?”

I could've given a hint last week and said one of the envelopes has $489 in it.

And the other nine have $1, $2, $4, $8, $16, $32, $64, $128, and the ninth envelope has $256. If you add those up -- 256, 128, 64, 32 -- you come up with 511, because in base 2, the next number would be…

512, OK? Two to the tenth would be 512, but he couldn't put 512 because you don't have it in there.

So you could put 489. So you can get any possible number between one and 511 by using the first nine envelopes, and then anything beyond 511 up to a 1,000 using 489 plus one gives you 490, 490 plus two gives you, and da-da-da.

Pretty good, huh? Give me my thousand bucks back. It was only a loan.

You can't do it unless the number is two. There you go, see? The power of two. Right?

 

[Sabertooth]

The Top Secret Free Beer Code
RAY: Interestingly, this was sent in by an "anonymous donor" who didn't want his or her name associated with the puzzler in any way, shape, or form.

Here it is:

There's this unusual little bar, where you can get a free beer if you know the secret code.

The secret code works like this: you sit down at the bar. The bartender tells you a number. And you tell him another number. If it's right, you get a free beer.

For example, a customer goes up to the bar and the bartender says, "six." The customer says, "three," and he gets his free beer.

The second fellow goes up to the bar, and the bartender says, "twelve." The customer says, "six," and he gets his free beer!

A third customer sits at the bar, and the bartender says, "fourteen." The customer says, "eight." He gets a free beer.

You're sitting there. The bartender turns to you and says, "twenty-two."

What do you say?

 

[Sabertooth]

I guess nine or ten.*

Spoiler: Why...?

The previous answers were the number of letters or characters in the "challenge" number.

*It is not clear if the hyphen counts in "twenty-two."

 

[Sabertooth]

The Top Secret Free Beer Code
RAY: Interestingly, this was sent in by an "anonymous donor" who didn't want his or her name associated with the puzzler in any way, shape, or form.

Here it is:

There's this unusual little bar, where you can get a free beer if you know the secret code.

The secret code works like this: you sit down at the bar. The bartender tells you a number. And you tell him another number. If it's right, you get a free beer.

For example, a customer goes up to the bar and the bartender says, "six." The customer says, "three," and he gets his free beer.

The second fellow goes up to the bar, and the bartender says, "twelve." The customer says, "six," and he gets his free beer!

A third customer sits at the bar, and the bartender says, "fourteen." The customer says, "eight." He gets a free beer.

You're sitting there. The bartender turns to you and says, "twenty-two."

What do you say?

Answer:
RAY: If you were the customer and said nine, you'd get a free beer. That's how many letters there are in "twenty-two."

 

[Sabertooth]

No-Brainer of a Non-Starter
RAY: This puzzler came from someone named Rob, who used to work for Applied Logic. Unauthorized use of company e-mail. Rob says:

"My wife owns a 1992 Olds Achieva with a quad-four, five-speed manual transmission and power everything. One morning, she's heading out to work, and her car won't start. I go out and listen as she tries to start the car. She turns the key. Not even a click. Being in a hurry, she takes my car. I put the battery charger on her car, and later in the day, I go out and I start it right up.

I drive it around a bit to charge the battery. Everything's fine. The next day, the exact same thing happens. I find instructions for determining if there's a drain on the battery. There's no drain. So, I buy a new battery.

Still, the problem persists. I jump-start the car and drive to the dealer. The dealer can't find a thing -- and charges us $10. We told them to let it sit there overnight and try it in the morning. They called the next morning and said what?"

So, we go to the dealer. My wife gets in with her keys -- and it won't start. We're standing there scratching our heads -- at which point, I ask her, "Did you just buy something for your car?"

And she says, "Yes!"

What did she buy?

 

[Sabertooth]

(I am probably overthinking this...)

Spoiler: My Guess

She bought a copy of her key without a security chip in it.

 

[Sabertooth]

No-Brainer of a Non-Starter
RAY: This puzzler came from someone named Rob, who used to work for Applied Logic. Unauthorized use of company e-mail. Rob says:

"My wife owns a 1992 Olds Achieva with a quad-four, five-speed manual transmission and power everything. One morning, she's heading out to work, and her car won't start. I go out and listen as she tries to start the car. She turns the key. Not even a click. Being in a hurry, she takes my car. I put the battery charger on her car, and later in the day, I go out and I start it right up.

I drive it around a bit to charge the battery. Everything's fine. The next day, the exact same thing happens. I find instructions for determining if there's a drain on the battery. There's no drain. So, I buy a new battery.

Still, the problem persists. I jump-start the car and drive to the dealer. The dealer can't find a thing -- and charges us $10. We told them to let it sit there overnight and try it in the morning. They called the next morning and said what?"

So, we go to the dealer. My wife gets in with her keys -- and it won't start. We're standing there scratching our heads -- at which point, I ask her, "Did you just buy something for your car?"

And she says, "Yes!"

What did she buy?

Answer:
RAY: Here's the answer. Rob's wife had bought new floor mats. She had an Olds Achieva with a quad four engine and a five-speed manual transmission. And because she has a manual transmission she has a starter inhibit switch attached to her clutch pedal, which prevents the starter from engaging unless the pedal is depressed all the way to the floor.

And when she puts the new floor mat in, it prevented her from pushing the clutch far enough down. But when Rob gets in with his big legs, he has no trouble mashing this pedal to the floor.

So all she had to do was cut a piece off of the floor mat or pull it back a little bit, and voila! The car started. All the hints were there.

 

[Sabertooth]

Stack the Deck
RAY: Let's say you have two ordinary decks of playing cards, minus the jokers. So, you have a deck of 52 cards and another deck of 52 cards.

Same color? The backs of them are red. And the other sides, the business sides are the same. So you take them and you shuffle them up--mix them all up as best you can.

Both decks together, so one hundred four cards.

And then you divide them into two equal piles. So, you've got a pile of 52 on one side of the table, and a pile of 52 on the other side of the table. Are you with me so far?

So, I've shuffled 104 cards together, and I've split them back into two piles of 52 each, and I've got one pile here on my left, and one pile to my right.

What are the chances that the number of red cards in pile A equals the number of black cards in pile 2? That's part one of the question. And then part two of the question: how many cards would you have to look at to be certain of your answer?

 

[Sabertooth]

Spoiler: My Guess

1. 100%
2. 0

Spoiler: Why?

For two such decks, there are a total of

• 52 red cards &
• 52 black cards.

Pile #1 has x red cards.
All remaining cards are black (52 - x).

Pile #2 has all of the remaining red cards (52 - x).
Subtracting those red cards from Pile #2,
52 - (52 - x) = 52 - 52 + x = x [black cards]
Pile #2 will always have the same number of black cards as Pile #1 has red cards.

(The same math applies if you calculate the number of black cards not found in Pile #1.)