I was hoping for some mathematical explanation as to why that was the cut-off! Not that kind of quiz, I realise.

So was I. As Tom Magliozzi would have said, that answer was bo-o-o-o-gus!

I googled it to see if anybody had a mathematical answer and this is what I got (paraphrased from Wikipedia):

According to Schur's theorem, any sufficiently large integer can be expressed as a linear combination of three relative primes (relative primes are numbers that share no common. so this is not correct for this example as 6 and 20 do share another common divider: 2, but close enough for our purpose). So it's a matter to find the lowest integer that can not be expressed as this number (the largest non-McNugget number. In Maths this is known as the Coin Problem). As we've seen from the answers that is 43.

Now to prove that 43 is the highest possible number, we can see that the next 6 numbers *are* possible to express in a combination of the three numbers:
44 = 6 + 9 + 9 + 20
45 = 9 + 9 + 9 + 9 + 9
46 = 6 + 20 + 20
47 = 9 + 9 + 9 + 20
48 = 6 + 6 + 9 + 9 + 9 + 9
49 = 9 + 20 + 20

So any larger number from then on than can be expressed as one of these numbers + x boxes of 6.

For combinations of 2 numbers, we can find the largest "McNugget"-number through a formula, but for combinations of 3 numbers, there is no formula (yet) and it remains trial and error.

Now McDonald's has issued boxes of 4 as well, so our largest McNugget-number now has become? (See spoiler for answer)

I've missed a few weeks, so we have a plethora of puzzlers today! First, congrats to outsider for getting this one correct.



The official answer:

TOM: I know the answer. It was Daylight Saving Time.

RAY: Bingo.

TOM: Doesn't that happen in the middle of the night?

RAY: That's when she left work. She left work at 1:30 AM, and 2:00 AM is when you make the change.

TOM: Oh, she works nights. That's very good!


Now, new Puzzler #1:

Ray: This was sent in by a fellow named Chuck Thompson from Austin, Texas. Zeke and Zack were two high-school buddies who lived close to each other and one day, they went off in search of after-school employment. Neither of them had a particularly reliable car so they decided to get a job at the same place so they could help each other get to work. Finding employment together proved harder than they had thought, until they happened upon a pig farmer who was impressed with their manure shoveling prowess.

"Can you start tomorrow?" he asked.

"Yes, sir!" they said.

"Do you have a car?"

"Yes, in fact each of us has a car," said Zeke, "but mine has a touchy fuel pump and a probability of starting of 80%. And Zack's starter has been acting up and the probability of his car starting is only 70%."

The farmer thought for a minute and said, "Sorry, boys, but my pigs and I need both of you here at least 90% of the time. Things pile up, you know. I'm afraid I can't hire you."

Well, with long faces they walked away bemoaning their bad luck. Who wouldn't want to spend his free time shoveling pig manure, right? But in an instant, they figured something out. They would have those dream jobs after all. What did they say to the farmer that got them hired?



New Puzzler #2:

RAY: A friend of ours who runs, for lack of a better term, a small business in our fair city -- he's a loan shark actually -- came across this word some years ago and sent it to Tom, thinking it might be a good puzzler. Tom obviously lost it. But he also sent it to Alan Feldman, who recently sent it to me!

Here it is:

Give me a word with three, consecutive double letters. I'll give you a couple of words that almost qualify, but don't. For example, the word committee, c-o-m-m-i-t-t-e-e. It would be great except for the i that sneaks in there. Or Mississippi -- M-i-s-s-i-s-s-i-p-p-i. If you could take out those i's it would work. But there is a word that has three consecutive pairs of letters and to the best of my knowledge this may be the only word. Of course there are probably 500 more but I can only think of one. What is the word?


and new Puzzler #3:

RAY: This puzzler was sent in by Ben Hayes, and he says it's a true story. Well, it probably was until I monkeyed around with it. So it's based on a true story.

I was in the market for a new car a few years ago and I decided early one Saturday morning to go do it. I wanted a Toyota Corolla, and who wouldn't, considering their stellar reputation and all that. So with that in mind I headed for the biggest, baddest Toyota dealership in the county. I figured they'd have the best selection and probably the best prices too, right? So I pulled up to the dealership in my clunker and the salesman, sensing an easy sale, met me in the parking lot. In fact he practically tripped over himself to get to me. And while he was pumping my hand vigorously, I told him I wanted a new Corolla with AC and power steering; the color didn't really matter, but I wanted manual transmission.

"You do?"

"Yeah, yeah, I do."

"Sheesh, we don't sell manuals at all. Practically all the cars we sell are automatics. We may have one or two on the lot. But -" and I sensed he was trying to get rid of me - "but our computer system is down this morning and the only way to find one is to go out into the lot and walk up and down the rows."

So I said, "Let's go for it!"

Well, I couldn't believe how many Corollas they had. Together we walked down a long row of Corollas. When we looked to the left there was a sea of rear bumpers and tailpipes. And when we looked to the right, more Corollas, these showing off their headlights and grilles. While I leisurely walked between these two rows of cars, the salesman bounced from one to another, looking in the windows to see what kind of shifter each car had.

And he tried to do it pretty efficiently, in that he would stand between two cars and he would look into the driver's window of one car and he'd look in the passenger window of the other car, so he was killing two birds with one stone. And then he'd run in front of me and run to the cars parked on my right. And he'd do the same thing, back and forth, back and forth. I, on the other hand, never got closer than 15 feet to any of these cars. And from my vantage point, there was absolutely no way I could possibly see into any of them. Yet at one point I said, "Oh, there's a stick shift."

The salesman walked up to it and said, "You're right! How did you know that?"

And the question is, how did I know that?

Bah. Dizzy D beat me to the first one. And I know squat about cars, so I don't know the third.


But if that pig farmer couldn't do the math about the cars starting by himself, maybe he needs a new bookkeeper, eh?

The answer turns out to be based on the US labeling rules for new cars:

RAY: Here's the answer. I knew it from the window sticker.

TOM: Yes you did.

RAY: The window sticker lists all the equipment in the car. Now at that distance, like 15 or 20 feet away, I couldn't possibly read standard shift.

TOM: But you could see the big mileage numbers.

RAY: Exactly. I could see the city mileage and the highway mileage. And all the automatics were the same, whatever they were, 27 and 34. And then when we got to the stick-shift car, it was 28, for example, and 36. And I knew it was a --

TOM: Just a slight difference.

RAY: Just a slight difference, a little better. And I knew that that car couldn't be an automatic, but it had to be a stick shift if it was a Corolla. Pretty good, huh?

TOM: Not bad!




And for this week, Ray wants us to do some calculating:

RAY: This is from my Lost Wages series and it was sent in by Katherine Curtis. She writes:

A man is visiting Las Vegas, known for gambling casinos and the like, and he falls for the local hype and heads for a casino with hopes of hitting it big.

He goes into this unusual casino that charges a dollar to enter, as well as a dollar to leave. He pays his dollar, plays the slot machines, loses half his money and in disgust pays his one dollar and leaves.

The following day he knows he'll do better. He takes the money he has left and heads out to the same casino. He pays his buck, but just like before, he again loses half his money, and pays another dollar to leave.

On the third day he figures he'll give it one more shot but his money is dwindling fast. The same thing happens. After paying his one dollar entrance, he loses half his money, and then pays his last dollar to get out. He's flat broke when he leaves.

So the question is: How much money did he start with?

If he'd gambled away the last dollar, he would have been in a different Puzzler.