I saw an ad at the quickie mart the other day that said you can combine soda with flavoring. They had 10 different types of soda, with 3 different types of flavoring (lemon, vanilla, and cherry).
Assuming you can mix any flavor combo with any soda, but you cannot mix soda, how many combinations are there? What’s the solution for an arbitrary number of sodas and flavorings?
2.
Martin
@jrg: Well, my teenage son would instantly answer ’69!’, but you know…
Can you mix more than one kind of flavoring? If so, there are 8 different flavorings (lemon, vanilla, cherry, lemon-vanilla, lemon-cherry, vanilla-cherry, lemon-vanilla-cherry plus no flavor) and 10 kinds of soda, so 80. If you can’t mix more than one flavoring then 40.
So in the first case, the answer is (flavor + 1)! * soda. In the second case, it’s just (flavor + 1) * soda.
3.
Steeplejack
Night shift checking in.
Damn! I could have answered that soda question.
It’s a good night for 1940s spy thrillers on TCM. I DVR’d Night Train to Munich earlier, and Fred MacMurray and Joan Crawford are chewing up the scenery in Above Suspicion right now. But in a good way.
4.
Debbie(aussie)
So much stupid! Thought I was all lauged out by Sarah ‘statute of liberty’. But jeebus, laughter is so good for the soul.
5.
jrg
@Martin: You can mix flavors, or have no flavor at all. So, yes, I think there there are 8 flavor combinations for 3 types of flavor.
…But I don’t think the answer is (flavor + 1)! * soda.
Deer I’m pretty sure can’t read but geese that’s another story.
40-45 years ago I used to hunt ducks and geese out by Salton Sea. The area we went to has/had a large game refuge with a 4ft barbed wire fence and signs that this was a game refuge and of course there was no hunting near there. There was a hill about 250 feet high about an 1/8 of a mile west of the game refuge that we climbed once to watch. The geese would fly in at about 200-250 ft till they hit the fence line, they would dive very steeply, flare out and land. About 10 ft inside the game refuge. The white signs stood out like beacons as long as there was light so maybe they couldn’t read but they sure knew where it was safe.
7.
gregt
It’s 2^flavors * soda.
(flavor+1)! * soda would be 192 (4! * 8 = 32 * 8).
For each flavor you choose presence or absence in the drink (2 options). You make a choice for each flavor. Thus 2*2*2, or 2^flavors.
8.
tkogrumpy
I’m still waiting for John Cole to fluff the Venazualan flag.
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Let’s chat about how President Obama is absolutely kicking Teabag ass and taking Republican names on the debt ceiling issue. It’s like he’s trying to see how much heat these bastards can take before they burst into flames!
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@jrg: Doh! Should never mix optimizing SQL with math. gregt corrected me.
15.
kdaug
Hm. I’ve also noted that my conspicuously posted sign to the dogs, stating – in clear language, mind you – that “No dog is permitted to lick their balls and/or assholes in clear view of human beings” is being generally ignored.
I’ve considered stenciling it on the front wall in large block letters, but I’m not sure that’s getting to the crux of the matter.
The sign is, after all, posted where everyone can see it.
Oh, you avoiding the content of my comment again. Yawn.
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19.
jon
The solution is obvious: crossing guards. But how do you get one of those orange vests on a retired moose?
20.
Scott P.
There’s no way anyone would take soda with no flavoring. If you allow that, you might as well allow double cherry, double cherry with vanilla, etc. in which case there are an infinite number of combinations.
21.
Tim I
I can’t stop laughing! I think I may have hurt myself.
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jrg
I saw an ad at the quickie mart the other day that said you can combine soda with flavoring. They had 10 different types of soda, with 3 different types of flavoring (lemon, vanilla, and cherry).
Assuming you can mix any flavor combo with any soda, but you cannot mix soda, how many combinations are there? What’s the solution for an arbitrary number of sodas and flavorings?
Martin
@jrg: Well, my teenage son would instantly answer ’69!’, but you know…
Can you mix more than one kind of flavoring? If so, there are 8 different flavorings (lemon, vanilla, cherry, lemon-vanilla, lemon-cherry, vanilla-cherry, lemon-vanilla-cherry plus no flavor) and 10 kinds of soda, so 80. If you can’t mix more than one flavoring then 40.
So in the first case, the answer is (flavor + 1)! * soda. In the second case, it’s just (flavor + 1) * soda.
Steeplejack
Night shift checking in.
Damn! I could have answered that soda question.
It’s a good night for 1940s spy thrillers on TCM. I DVR’d Night Train to Munich earlier, and Fred MacMurray and Joan Crawford are chewing up the scenery in Above Suspicion right now. But in a good way.
Debbie(aussie)
So much stupid! Thought I was all lauged out by Sarah ‘statute of liberty’. But jeebus, laughter is so good for the soul.
jrg
@Martin: You can mix flavors, or have no flavor at all. So, yes, I think there there are 8 flavor combinations for 3 types of flavor.
…But I don’t think the answer is (flavor + 1)! * soda.
Ruckus
Deer I’m pretty sure can’t read but geese that’s another story.
40-45 years ago I used to hunt ducks and geese out by Salton Sea. The area we went to has/had a large game refuge with a 4ft barbed wire fence and signs that this was a game refuge and of course there was no hunting near there. There was a hill about 250 feet high about an 1/8 of a mile west of the game refuge that we climbed once to watch. The geese would fly in at about 200-250 ft till they hit the fence line, they would dive very steeply, flare out and land. About 10 ft inside the game refuge. The white signs stood out like beacons as long as there was light so maybe they couldn’t read but they sure knew where it was safe.
gregt
It’s 2^flavors * soda.
(flavor+1)! * soda would be 192 (4! * 8 = 32 * 8).
For each flavor you choose presence or absence in the drink (2 options). You make a choice for each flavor. Thus 2*2*2, or 2^flavors.
tkogrumpy
I’m still waiting for John Cole to fluff the Venazualan flag.
jrg
@gregt: Yes. I think that’s right.
Cliff in NH
I invite comments on the Banksters thread:
https://balloon-juice.com/2011/06/01/banksters-caught-in-the-immigration-crossfire/#comment-2614235
Dennis G.
That is a thing of beauty.
Uncle Clarence Thomas
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Let’s chat about how President Obama is absolutely kicking Teabag ass and taking Republican names on the debt ceiling issue. It’s like he’s trying to see how much heat these bastards can take before they burst into flames!
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piratedan
@jrg: grape
Martin
@jrg: Doh! Should never mix optimizing SQL with math. gregt corrected me.
kdaug
Hm. I’ve also noted that my conspicuously posted sign to the dogs, stating – in clear language, mind you – that “No dog is permitted to lick their balls and/or assholes in clear view of human beings” is being generally ignored.
I’ve considered stenciling it on the front wall in large block letters, but I’m not sure that’s getting to the crux of the matter.
The sign is, after all, posted where everyone can see it.
Uriel
@Uncle Clarence Thomas:
Oh, you again.
Yawn.
FlipYrWhig
@Uriel:
.
.
I know you are.
But what am I.
Obama bad.
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Uncle Clarence Thomas
@Urinal:
.
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Oh, you avoiding the content of my comment again. Yawn.
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jon
The solution is obvious: crossing guards. But how do you get one of those orange vests on a retired moose?
Scott P.
There’s no way anyone would take soda with no flavoring. If you allow that, you might as well allow double cherry, double cherry with vanilla, etc. in which case there are an infinite number of combinations.
Tim I
I can’t stop laughing! I think I may have hurt myself.