Mathematicians, Is this even possible?
03-01-20, 07:37 AM
#2
DVD Talk Legend
Re: Mathematicians, Is this even possible?
Easily. There are 39 one-topping pizzas.
There are 39x39 = 1521 two-topping pizzas, including two of the same toppings.
39x39x39 = 59,319 three-topping pizzas.
39x39x39x39 = 2,313,441 four-topping pizzas.
Four toppings is halfway there, exponentially speaking. Eight-toppings is 5 trillion.
There are 39x39 = 1521 two-topping pizzas, including two of the same toppings.
39x39x39 = 59,319 three-topping pizzas.
39x39x39x39 = 2,313,441 four-topping pizzas.
Four toppings is halfway there, exponentially speaking. Eight-toppings is 5 trillion.
Last edited by Nick Danger; 03-01-20 at 07:45 AM.
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03-01-20, 08:02 AM
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Re: Mathematicians, Is this even possible?
Originally Posted by Nick Danger
Easily. There are 39 one-topping pizzas.
There are 39x39 = 1521 two-topping pizzas, including two of the same toppings.
39x39x39 = 59,319 three-topping pizzas.
39x39x39x39 = 2,313,441 four-topping pizzas.
Four toppings is halfway there, exponentially speaking. Eight-toppings is 5 trillion.
There are 39x39 = 1521 two-topping pizzas, including two of the same toppings.
39x39x39 = 59,319 three-topping pizzas.
39x39x39x39 = 2,313,441 four-topping pizzas.
Four toppings is halfway there, exponentially speaking. Eight-toppings is 5 trillion.
03-01-20, 08:07 AM
#6
DVD Talk Legend
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.
39 options
1 combo of 0,
39 combos of 1,
714 combos of 2,
etc.
03-01-20, 08:11 AM
#7
DVD Talk Legend
Re: Mathematicians, Is this even possible?
Originally Posted by Defiant
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.
03-01-20, 08:12 AM
#8
DVD Talk Legend
Re: Mathematicians, Is this even possible?
Originally Posted by Defiant
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.
03-01-20, 08:17 AM
#9
DVD Talk Legend
Re: Mathematicians, Is this even possible?
Originally Posted by Dan
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.
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"?
03-01-20, 08:32 AM
#10
DVD Talk Legend
Re: Mathematicians, Is this even possible?
Originally Posted by Nick Danger
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"?
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)
03-01-20, 08:53 AM
#11
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.
03-01-20, 09:43 AM
#13
DVD Talk Hero
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 half-pizzas.
But that numbers will launch into the stratosphere when start doing double and half-toppings.
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 half-pizzas.
But that numbers will launch into the stratosphere when start doing double and half-toppings.
03-01-20, 11:24 AM
#17
Moderator
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.
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.
03-01-20, 12:05 PM
#18
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.
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.
03-01-20, 01:28 PM
#20
DVD Talk Legend
Re: Mathematicians, Is this even possible?
Originally Posted by bluetoast
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.
03-01-20, 02:58 PM
#21
DVD Talk Hero
Re: Mathematicians, Is this even possible?
Yeah, we're looking at something like 300 sextillion different pizzas if we're half-and-halfing them.
In scientific notation, that's 3x10^23.
300,000,000,000,000,000,000,000.
In scientific notation, that's 3x10^23.
300,000,000,000,000,000,000,000.
03-01-20, 03:01 PM
#22
DVD Talk Legend
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. 
0101001
0101001
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03-01-20, 03:51 PM
#24
DVD Talk Legend
Re: Mathematicians, Is this even possible?
Looks like we have a few people here who have a better memory of Finite than I do.
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.
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.
