Chicken McNugget problem
January 17th, 2011 at 8:50:29 AM
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One of wizard's site, mathproblems.info, it has this Chicken McNugget problem:
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At McDonalds you can order Chicken McNuggets in boxes of 6, 9, and 20. What is the largest number such that you can not order any combination of the above to achieve exactly the number you want?
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The answer wizard gave is 43. Does the wizard mean smallest number? not the largest?
I thought the largest will be any big prime number, meaning the answer is infinite...
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At McDonalds you can order Chicken McNuggets in boxes of 6, 9, and 20. What is the largest number such that you can not order any combination of the above to achieve exactly the number you want?
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The answer wizard gave is 43. Does the wizard mean smallest number? not the largest?
I thought the largest will be any big prime number, meaning the answer is infinite...
January 17th, 2011 at 9:00:54 AM
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No, Wizard is right. You can make all sorts of prime numbers by ADDING up chicken mcnugget boxes. 20 + 9 = 29, which is prime. 9*3 +3*20 = 97 which is prime. And so forth.
EDIT: since 93 isn't prime... I will pick 97 as my next example, which I'm pretty sure is.
His solution pretty rigourously explains how you can be absolutely sure there are no numbers hiding above 43 that can't be made.
EDIT: since 93 isn't prime... I will pick 97 as my next example, which I'm pretty sure is.
His solution pretty rigourously explains how you can be absolutely sure there are no numbers hiding above 43 that can't be made.
Wisdom is the quality that keeps you out of situations where you would otherwise need it
January 17th, 2011 at 11:06:04 AM
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One problem with this is that McDonald's now has 10 piece boxes instead of 9 piece boxes, so the parameters have changed.
"Bite my Glorious Golden Ass!" - Bender Bending Rodriguez
January 17th, 2011 at 11:57:33 AM
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93 is prime? (31 x 3)
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You want the truth! You can't handle the truth!
January 17th, 2011 at 12:01:56 PM
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Not only that, many McDonalds now have a 4 piece on the Dollar Menu!Quote: Toes14One problem with this is that McDonald's now has 10 piece boxes instead of 9 piece boxes, so the parameters have changed.
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http://www.DaveMillerGaming.com/ —————————————————————————————————————
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
January 17th, 2011 at 12:10:12 PM
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The bigger question is why would anyone want to eat so many Chicken McNuggets?
All animals are equal, but some are more equal than others
January 17th, 2011 at 12:21:29 PM
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ah...my bad
January 17th, 2011 at 12:44:23 PM
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No, no, the answer is easy. You buy two 20s, and one 6. Then you open up the box of 6 and feed three of them to the dog. Voila! You have 43.
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
January 17th, 2011 at 2:16:47 PM
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Quote: mkl654321No, no, the answer is easy. You buy two 20s, and one 6. Then you open up the box of 6 and feed three of them to the dog. Voila! You have 43.
I think the key word is ORDER. In your example, you ordered 46 McNuggets, not 43.
"Bite my Glorious Golden Ass!" - Bender Bending Rodriguez
January 17th, 2011 at 7:26:07 PM
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Quote: Toes14I think the key word is ORDER. In your example, you ordered 46 McNuggets, not 43.
Okay, you bribe the cook to put an extra 3 nuggets in one of your two boxes of 20.
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
January 17th, 2011 at 9:01:43 PM
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The question is what is the largest number that you CAN'T order from boxes of 6, 9, and 20.
I've had people challenge me from time to time, throwing huge primes at me. However, it is easy to fill most of the order with 20-piece boxes, and use 6-piece and 9-piece boxes to get to the target exactly. Give me any number bigger than 43 and I'll show you an answer.
On a more practical note, a friend of mine once made a bet that he could eat 100 McNuggets. I think he got to 86 when he admitted defeat.
I've had people challenge me from time to time, throwing huge primes at me. However, it is easy to fill most of the order with 20-piece boxes, and use 6-piece and 9-piece boxes to get to the target exactly. Give me any number bigger than 43 and I'll show you an answer.
On a more practical note, a friend of mine once made a bet that he could eat 100 McNuggets. I think he got to 86 when he admitted defeat.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 17th, 2011 at 9:05:29 PM
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Quote: Wizarda friend of mine once made a bet that he could eat 100 McNuggets. .
Good god. The damn things are dry and tasteless, they taste like whatever you dip them in. Yuk.
"It's not called gambling if the math is on your side."
January 17th, 2011 at 9:20:23 PM
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Quote: EvenBobGood god. The damn things are dry and tasteless, they taste like whatever you dip them in. Yuk.
I could say the same thing, but must admit, I loved McDonalds as a kid. Who didn't? Even in college, I don't think I could get to 100, but would have enjoyed the challenge. In my prime I think I could have easily made 60.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 17th, 2011 at 9:22:54 PM
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Quote: WizardThe question is what is the largest number that you CAN'T order from boxes of 6, 9, and 20.
I've had people challenge me from time to time, throwing huge primes at me. However, it is easy to fill most of the order with 20-piece boxes, and use 6-piece and 9-piece boxes to get to the target exactly. Give me any number bigger than 43 and I'll show you an answer.
On a more practical note, a friend of mine once made a bet that he could eat 100 McNuggets. I think he got to 86 when he admitted defeat.
So what is it about the relationships of those numbers and the number 43? The LCM of 6, 9, and 20 is 180, which for some reason makes me think that has something to do with the answer, but I'm at a loss to say why.
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
January 17th, 2011 at 9:24:48 PM
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Quote: WizardI could say the same thing, but must admit, I loved McDonalds as a kid.
I loved Mc's as a teen because I could get 4 burgers and 4 fries for $1.25, which lasted to about 1968 when they raised it to 20 cents each.
"It's not called gambling if the math is on your side."
January 17th, 2011 at 9:59:26 PM
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Quote: mkl654321So what is it about the relationships of those numbers and the number 43? The LCM of 6, 9, and 20 is 180, which for some reason makes me think that has something to do with the answer, but I'm at a loss to say why.
I think you're overthinking it. Here is my solution.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 18th, 2011 at 4:51:14 AM
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6 chicken mcnuggets weigh 114g (source). 310 calories, 21g of fat, and 670 mg of sodium.
Multiply by 100/6, to get:
1900g, 5167 calories, 350g of fat, 11167mg of sodium.
4.2 lbs, double the average daily calorie intake, over 5 times your recommended daily fat intake, and over 4.5 times your recommended sodium intake.
Gross.
Multiply by 100/6, to get:
1900g, 5167 calories, 350g of fat, 11167mg of sodium.
4.2 lbs, double the average daily calorie intake, over 5 times your recommended daily fat intake, and over 4.5 times your recommended sodium intake.
Gross.
Wisdom is the quality that keeps you out of situations where you would otherwise need it
January 18th, 2011 at 4:58:32 AM
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The significance is that you have both even and odd package sizes. Therefore, there is a maximum number of nuggets, 43, that you can't achieve when you combine those package sizes.Quote: mkl654321So what is it about the relationships of those numbers and the number 43? The LCM of 6, 9, and 20 is 180, which for some reason makes me think that has something to do with the answer, but I'm at a loss to say why.
As was already mentioned, McDonalds now has a 4 piece box, and in some locations have dropped the 9 piece box. (Some have replaced it with a 10 piece box.)
That being the case, it's easy to see that with a 4, 6, and 20 piece choices, you can combine to make any even number of nuggets except 2. It's irrelevant that the LCM is 60.
I invented a few casino games. Info:
http://www.DaveMillerGaming.com/ —————————————————————————————————————
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
January 19th, 2011 at 3:37:35 PM
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The posts about the challenge to eat 100 Chicken McNuggets has been moved to Chicken McNugget Eating Challenge.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 19th, 2011 at 3:39:52 PM
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I'm still trying to find an algebraic solution for a general case of x, y, and z packs.
Here is what I have so far. If x and y are both prime, then the largest number of McNuggets you can't exactly buy is xy - x - y.
Here is what I have so far. If x and y are both prime, then the largest number of McNuggets you can't exactly buy is xy - x - y.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 19th, 2011 at 7:29:28 PM
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Quote: WizardSorry to keep talking to myself in this thread, but according to Wikipedia there is no known solution for the case of 3 or more box sizes of McNuggets.
You should find the solution, then anounce it but never publish it: The Wizard's Last Theorem.
Donald Trump is a fucking criminal
January 19th, 2011 at 7:32:35 PM
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Quote: WizardSorry to keep talking to myself in this thread, but according to Wikipedia there is no known solution for the case of 3 or more box sizes of McNuggets.
That's probably a good thing. No-one buying McNuggets should be faced with more than 3 choices of box size.
If nothing will change then I am nothing.
