Deadman31

1 trillion? How would they determine?

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.

Deadman31

Just seems ludicrous to me

Nick Danger

Ludicrous that they would sell a pizza with 8 toppings of pepperoni? Sure. But it doesn't make the claim false.

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.

Dan

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.

Nick Danger

Double pepperoni is a two-topping pizza for the sake of the calculation. People do order it. Besides, I'm too lazy to do the permutation of 39 toppings taken 8 at a time. It's 39!/(39-8)! if I remember my high school math.

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.

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"?

Dan

From 0 to 39 toppings (no duplicates), the permutations are:
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)

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.

Dan

I just want some of that XXX cheese

Josh-da-man

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.

Deadman31

I think they made up a bullshit number figuring nobody would counteract them. They were wrong

Decker

Hamburg?

E Unit

6 is the answer.

Pharoh

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.

grundle

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.

kd5

The correct answer is 42.

Nick Danger

So if you allow for half-and-half pizzas, the total is 500 billion times 500 billion.

Josh-da-man

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.

Vibiana

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

Deadman31

When they booted me, I told them the dress was blue

Norm de Plume

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.

DVD Polizei

I can think of a trillion reasons why that ad sucks.

But I won't because it will hurt.