Mathematicians, Is this even possible?

Re: Mathematicians, Is this even possible?
Easily. There are 39 onetopping pizzas.
There are 39x39 = 1521 twotopping pizzas, including two of the same toppings. 39x39x39 = 59,319 threetopping pizzas. 39x39x39x39 = 2,313,441 fourtopping pizzas. Four toppings is halfway there, exponentially speaking. Eighttoppings is 5 trillion. 
Re: Mathematicians, Is this even possible?
Just seems ludicrous to me

Re: Mathematicians, Is this even possible?
Ludicrous that they would sell a pizza with 8 toppings of pepperoni? Sure. But it doesn't make the claim false.

Re: Mathematicians, Is this even possible?
Originally Posted by Nick Danger
(Post 13695838)
Easily. There are 39 onetopping pizzas.
There are 39x39 = 1521 twotopping pizzas, including two of the same toppings. 39x39x39 = 59,319 threetopping pizzas. 39x39x39x39 = 2,313,441 fourtopping pizzas. Four toppings is halfway there, exponentially speaking. Eighttoppings is 5 trillion. 
Re: Mathematicians, Is this even possible?
1,672,219,813,000 ish. (assuming no doubles, triples, etc. for each topping)
39 options 1 combo of 0, 39 combos of 1, 714 combos of 2, etc. 
Re: Mathematicians, Is this even possible?
Originally Posted by Defiant
(Post 13695845)
Close, but you've got a minor error. It would be 39x38 = 1482 two topping pizzas. (Having olives+olives is not a two topping pizza). And 39x38x37 for three, and so on.

Re: Mathematicians, Is this even possible?
Originally Posted by Defiant
(Post 13695845)
Close, but you've got a minor error. It would be 39x38 = 1482 two topping pizzas. (Having olives+olives is not a two topping pizza). And 39x38x37 for three, and so on.
Once you get half way (19 toppings) the permutations start to go down again too, because of this. 
Re: Mathematicians, Is this even possible?
Originally Posted by Dan
(Post 13695848)
Close, but you have to halve that as well because pepperoni + mushroom is the same as mushroom + pepperoni.
Once you get half way (19 toppings) the permutations start to go down again too, because of this. So how many toppings does it take to reach one trillion? Do you have to go all the way to "one with everything"? 
Re: Mathematicians, Is this even possible?
Originally Posted by Nick Danger
(Post 13695849)
I agree that I did that wrong.
So how many toppings does it take to reach one trillion? Do you have to go all the way to "one with everything"? 1 39 741 9139 82251 575757 3262623 15380937 61523748 211915132 635745396 1676056044 3910797436 8122425444 15084504396 25140840660 37711260990 51021117810 62359143990 68923264410 68923264410 62359143990 51021117810 37711260990 25140840660 15084504396 8122425444 3910797436 1676056044 635745396 211915132 61523748 15380937 3262623 575757 82251 9139 741 39 1 Note that the permutations in the middle may not be 100% accurate for the last digit. They end in 0 because of how they're displayed on my calculator (ie: 6.892326441 E+10) 
Re: Mathematicians, Is this even possible?
Don‘t forget that you can (at most pizza places) split the pizza in half and do different toppings on each half. So it’s every combination ever, and then you add that with every combination ever, permutated with every other combination ever.

Re: Mathematicians, Is this even possible?
I just want some of that XXX cheese other

Re: Mathematicians, Is this even possible?
If you had 39 toppings available, wouldn't the number of combinations be 2^39?
Think of a pizza like a binary number: 000000000000000000000000000000000000000 where a zero represents the absence of a topping and a one represents the topping on the pizza. If they don't limit the number of toppings per pizza and you can get as many as you want (which, with 39 options would be more like a big pile of meats and vegetables on a piece of bread), then it works out to a bit over 500 billion  not counting double portions or halfpizzas. But that numbers will launch into the stratosphere when start doing double and halftoppings. 
Re: Mathematicians, Is this even possible?
I think they made up a bullshit number figuring nobody would counteract them. They were wrong

Re: Mathematicians, Is this even possible?
Hamburg?

Re: Mathematicians, Is this even possible?
6 is the answer.

Re: Mathematicians, Is this even possible?
Rough math and Mathematica says the correct answer is 549,755,813,887
Formula: 39!/1!(38!)+39!/2!(37!)....39!/39!(0!) It is an N choose K formula, but you need to sum each specific instance of K. 
Re: Mathematicians, Is this even possible?
If p is the number of possible toppings, then the number of different possible combinations is 2^p. In order to have one trillion possible combinations, you would need to have at least 40 different possible toppings, because 40 is the smallest number p where (2^p) >= one trillion.
That list has 39 toppings. So with 39 possible toppings, no, it is not possible to have one trillion different combinations. If there were 40 toppings, then yes, it would be possible to have one trillion different combinations. 
Re: Mathematicians, Is this even possible?
The correct answer is 42.

Re: Mathematicians, Is this even possible?
Originally Posted by bluetoast
(Post 13695860)
Don‘t forget that you can (at most pizza places) split the pizza in half and do different toppings on each half. So it’s every combination ever, and then you add that with every combination ever, permutated with every other combination ever.

Re: Mathematicians, Is this even possible?
Yeah, we're looking at something like 300 sextillion different pizzas if we're halfandhalfing them.
In scientific notation, that's 3x10^23. 300,000,000,000,000,000,000,000. 
Re: Mathematicians, Is this even possible?
Okay, I barely made it through ninth grade algebra and I am now sharpening a slide rule in preparation for cutting my own throat. Goodbye, cruel world. :D
0101001 
Re: Mathematicians, Is this even possible?
When they booted me, I told them the dress was blue

Re: Mathematicians, Is this even possible?
Looks like we have a few people here who have a better memory of Finite than I do.:lol: It was the most practical math course I ever took, but it was an elective, and after a few weeks I was the only one left in the class.

Re: Mathematicians, Is this even possible?
I can think of a trillion reasons why that ad sucks.
But I won't because it will hurt. 
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