Chicken McNuggets are sold in boxes of 6, 9, and 20. What is the largest integer such that exactly that many McNuggets may not be purchased using some combination of these box sizes?

As always, please put answers and solutions in spoiler tags. Free 20-pack to the first correct answer.

x=any integer

N=integer number of nuggets

For N>=6 and N=3x, combinations of 6 and 9 do the trick.

For N>=26 and N=3x+1, combinations of 6 and 9 and one box of 20 will do it.

With two boxes of 20, combinations of 6 and 9 can get you to N=3x+2 for N>=46.

That should cover everything above 44.

Oops! Error.

Quote:Doc44

x=any integer

N=integer number of nuggets

For N>=6 and N=3x, combinations of 6 and 9 do the trick.

For N>=26 and N=3x+1, combinations of 6 and 9 and one box of 20 will do it.

With two boxes of 20, combinations of 6 and 9 can get you to N=3x+2 for N>=46.

That should cover everything above 44.

6 and 9 are both multiples of 3, so any combination without a 20 is a multiple of 3.

Any multiple of 6 is just that many 6s; except for 3, every multiple of 3 that is not a multiple of 6 is covered by a 9 and zero or more 6s.

Thus, the only positive multiple of 3 you can't get is 3.

1 20-piece is two more than a multiple of 3, and adding multiples of 3 keep the total at two more than a multiple of 3, so the largest number not possible that is two more than a multiple of 3 is 23.

2 20-pieces is one more than a multiple of 3, and adding multiples of 3 keep the total at one more than a multiple of 3, so the largest number not possible that is one more than a multiple of 3 is 43.

Since every number is either a multiple of 3, one more than a multiple of 3, or two more than a multiple of 3, the largest impossible number is 43.

Tell you what - if Doc is there tomorrow, you can give him the prize. I'm going through more than my share of McNuggets trying to get a set of the common Monopoly pieces (all I need now is St. Charles Place).

Do they still sell 9-piece boxes in Vegas? The only combinations where I live are 6s and 10s.

Quote:ThatDonGuyTell you what - if Doc is there tomorrow, you can give him the prize. I'm going through more than my share of McNuggets trying to get a set of the common Monopoly pieces (all I need now is St. Charles Place).

Do they still sell 9-piece boxes in Vegas? The only combinations where I live are 6s and 10s.

You are indeed correct. I have a feeling there will be plenty of leftover McNuggets at the challenge, but if not, and Doc wants them, I will grant your wish.

Will keep an eye out for St. Charles Place for you. I just came from Albertson's and they gave me two Monopoly things. Is this the same promotion?

I think they no longer sell the 20-piece box but can recall for years it was 6, 9, and 20.

Sorry but Chicken nuggets are sold in 4 piece boxes as well. Apparently 40 as well.Quote:WizardMath problem time!

Chicken McNuggets are sold in boxes of 6, 9, and 20. What is the largest integer such that exactly that many McNuggets may not be purchased using some combination of these box sizes?

As always, please put answers and solutions in spoiler tags. Free 20-pack to the first correct answer.

I think 4s are only in Happy Meals.Quote:AxelWolfSorry but Chicken nuggets are sold in 4 piece boxes as well.

Quote:AxelWolfSorry but Chicken nuggets are sold in 4 piece boxes as well.

He's correct.

Quote:WizardWill keep an eye out for St. Charles Place for you. I just came from Albertson's and they gave me two Monopoly things. Is this the same promotion?

No - entirely different game. Vons and Safeway has this one as well.

The McDonald's one uses properties from the game. The main way to win is to collect a set of properties; each set has one "rare" piece, so they can control how many of each prize they might give away. The rare ones are:

Mediterranean Avenue

Short Line (railroad)

Vermont Avenue

Virginia Avenue

Tennessee Avenue

Kentucky Avenue

Ventnor Avenue

Pennsylvania Avenue (not Pennsylvania Railroad, which is common)

Boardwalk

I'm sure that's the intended reason they started it, however you can order a 4 pack without any problem or rugrats in tow. I never had to say no happy meal.Quote:ThatDonGuyI think 4s are only in Happy Meals.

Give me a four piece, make it fresh!

Also I think I remember a 50 pack special deal.

Quote:ThatDonGuyI'm going through more than my share of McNuggets trying to get a set of the common Monopoly pieces (all I need now is St. Charles Place).

Quote:ThatDonGuyI think 4s are only in Happy Meals.

I'd like to see them offer a Happy Ending Meal.

it's a free box of Mcnuggets?

Quote:odiousgambit

it's a free box of Mcnuggets?

Oh my! I knew Henderson was liberal with that kind of thing, but to put it in writing surprises even me.

Quote:ThatDonGuyI think 4s are only in Happy Meals.

I stand corrected - where I live, the 4-piece box has replaced the 6, and it's on the "2 for $2.50" menu.

Also, I managed to get a St. Charles Place, so I "completed the set." For those of you joining the thread late, that's not the set of violet properties (worth $2000 this year)," but the set of 17 "common" pieces. Note that the rares are the same from one year to the next; my guess is, it's to crack down on scammers trying to sell "rare" pieces that would turn out to be common pieces from a previous year. (It could also be to make it easier to detect a cheater trying to use pieces from different years, but in that case, why bother keeping them the same when they switched the printing from portrait to landscape a few years ago?)

Is that a Happy Meal box, stuff to overflowing with McNuggets?Quote:GWAE

Is that supposed to make someone happy?

We're all looking for Boardwalk, as I don't think you even need to "match" them anymore... Boardwalk is an "instant winner" just like the other "pay" properties (2 of 3 are common and the 1 is the instant winner of them).Quote:djatcJust stopped at McDonalds, Monopoly is back. Are they on the nuggets? I'm looking for Boardwalk.

Quote:djatcJust stopped at McDonalds, Monopoly is back. Are they on the nuggets? I'm looking for Boardwalk.

Yes - a 10-piece has 2 stamps; a 20-piece has 4. You can also get 4 from a large fries, and 2 from a Big Mac, a medium drink, and a few other things.

Quote:RomesWe're all looking for Boardwalk, as I don't think you even need to "match" them anymore... Boardwalk is an "instant winner" just like the other "pay" properties (2 of 3 are common and the 1 is the instant winner of them).

They're not "instant winners" as you still need to collect the other piece(s) of that color, but getting the common pieces you need shouldn't be that hard; I got all 17 of them from 48 stamps.

However, if I read the rules right, for all intents and purposes, Boardwalk really is an "instant winner" as the only way the numbers crunch correctly is if the one Boardwalk piece in the game already comes attached to a Park Place.

Quote:RomesWe're all looking for Boardwalk, as I don't think you even need to "match" them anymore... Boardwalk is an "instant winner" just like the other "pay" properties (2 of 3 are common and the 1 is the instant winner of them).

I think they advertise 1 in 4 pieces are winners, most of them food. I wonder if there is any EV calculations for this..... I have comps I can use at McDonalds lol.

Quote:jml24Looking at that photo makes the challenge seem a lot more daunting. I have not eaten a McNugget in quite a few years and that photo does not look appetizing.

It's suppose to be chicken, but no one really knows.

I'm curious, who gets the prizes, if any, obtained by purchasing the 100 McNuggets for the challenge (20 stamps, total)? Wizard, because he's buying? Maybe PG can keep them as a bonus if he completes the challenge. Or maybe just the ones form the completed boxes if he falls short.Quote:ThatDonGuya 10-piece has 2 stamps; a 20-piece has 4.

Hope you have fun with the challenge. I'll be looking forward to the video!

Use your comps for the Nuggets and give Mike a small discount. Youhave just turned your comps into almost full cash value.Quote:djatcI think they advertise 1 in 4 pieces are winners, most of them food. I wonder if there is any EV calculations for this..... I have comps I can use at McDonalds lol.

AP move for sure.

Quote:kmumfAlright challenge number 5! I am always thinking I should do this when I head out to Vegas. I have a few eating challenges under my belt. Worst one was 5lbs of ghost pepper wings in 15 minutes I did it and could not see due to tears and face burning.

I agree. Yes, you should line up for this challenge. :)

For example:

Who could eat a bale of kale?

Don't eat sparsely, gorge on parsley.

Grin and bear it, feast on carrot.

Quote:MrVYou guys ever consider substituting a healthy food for the unhealthy fast food that McDonalds turns out?

I'm open to that. Specific ideas?

Seriously, as a healthy lifestyle advocate, I'm thinking about making #5 the last McNugget challenge.

Ah, how about ears of corn?

Quote:MrVYou guys ever consider substituting a healthy food for the unhealthy fast food that McDonalds turns out?

For example:

Who could eat a bale of kale?

Don't eat sparsely, gorge on parsley.

Grin and bear it, feast on carrot.

Who the hell wants to watch someone eat a bushel of broccoli. Part of the fun in this challenge is can someone not only eat the quantity of food but how will they deal with the grease.

Quote:WizardI'm open to that. Specific ideas?

Seriously, as a healthy lifestyle advocate, I'm thinking about making #5 the last McNugget challenge.

I would be very disappointed if you made that decision.

Quote: Wizard

I'm open to that. Specific ideas?

Seriously, as a healthy lifestyle advocate, I'm thinking about making #5 the last McNugget challenge.

Quote: DRich

I would be very disappointed if you made that decision.

Reply: The Feathered One

I am reserving judgement. Should PG actually survive this ordeal w/o lasting after effects other than slight mental trauma, I will approve a # 6. Like OG said ( just in case anyone cared what I thought ;-)

Quote:TwoFeathersATLApril 14th, 2016 at 10:08:44 AMpermalink

Quote: Wizard

I'm open to that. Specific ideas?

Seriously, as a healthy lifestyle advocate, I'm thinking about making #5 the last McNugget challenge.

Quote: DRich

I would be very disappointed if you made that decision.

Reply: The Feathered One

I am reserving judgement. Should PG actually survive this ordeal w/o lasting after effects other than slight mental trauma, I will approve a # 6. Like OG said ( just in case anyone cared what I thought ;-)

Reply: BBB (lol)

Um, so you've made money on #2,3, and 4 off me alone. Someone's going to pull this out for me, hopefully PG, but if not, I'm all for #6. Even if PG does win, I'm still for #6.

You're betting against every time; that doesn't make you an enabler. Just like one night's drinking or binge-ing or whatever doesn't make a person an alcoholic or food addict. You're not responsible for the rest of us in that way; nobody is. :)

Oh come on now, you also host a Red Rock hike and we know you're into physical sports and exercise.Quote:WizardI'm open to that. Specific ideas?

Seriously, as a healthy lifestyle advocate, I'm thinking about making #5 the last McNugget challenge.

Eating bad occasionally isn't a big deal. The reason the nugget challenge is interesting, because we have no clue what it is that makes it so difficult, yet people think they can actually do it. Some fail miserably. >>(Dj)<<

It just wouldn't be the same, please don't change tradition. If someone wants to do the challenge let them. If someone wants to eat something else instead that sounds good to.

I honestly don't think stuffing yourself with a bunch of anything is healthy.

There appears to be some free-roll money available for a successful attempt.

Who knows, maybe pancakes would go down (and stay down) easier than McNuggets?

;)

Quote:beachbumbabsI agree. Yes, you should line up for this challenge. :)

Ill see what happens this time and if its completed I might wait and see if the WIZ's healthy option happens.

Quote:WizardofnothingIf anyone needs it Sls has rooms available online tonight for 45 and tommorow for 41

That dump is still open?