# Mathematicians, Is this even possible?

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**26**Moderator

**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.

Close, but it is (2^n)-1. I went further earlier to hopefully illustrate the rationale.

Use a small number of choices and it is easy to see the minor error in your formula. Take 3 toppings. Your formula gives us 8 combinations, but there are clearly only 7 choices. Or go with only 2 toppings. 2^n would give us 4 combinations but in reality there are only 3.

And while 42 is always an acceptable answer, 549,755,813,887 is the correct answer.

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**27****Re: Mathematicians, Is this even possible?**

All of you math geeks are total losers. Also, more than 4 or 5 toppings on one pizza is horrible, especially if they are veggies.

My answer is 12.

My answer is 12.

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Kurt D (03-01-20)

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**29**Banned

**Re: Mathematicians, Is this even possible?**

Close, but it is (2^n)-1. I went further earlier to hopefully illustrate the rationale.

Use a small number of choices and it is easy to see the minor error in your formula.

And while 42 is always an acceptable answer, 549,755,813,887 is the correct answer.

Use a small number of choices and it is easy to see the minor error in your formula.

**Take 3 toppings. Your formula gives us 8 combinations, but there are clearly only 7 choices.**Or go with only 2 toppings. 2^n would give us 4 combinations but in reality there are only 3.And while 42 is always an acceptable answer, 549,755,813,887 is the correct answer.

1) Pepperoni

2) Sausage

3) Mushroom

4) Pepperoni and sausage

5) Pepperoni and mushroom

6) Sausage and mushroom

7) Pepperoni, sausage, and mushroom

8) No toppings

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Thread Starter

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**32**Moderator

**Re: Mathematicians, Is this even possible?**

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**33**DVD Talk Legend

Join Date: Aug 1999

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**Re: Mathematicians, Is this even possible?**

The number of possible combinations actually doubles IF you order the pizza and then call back to change the toppings.

Oh yeah, you only have 1/5th the number of combinations if you make it at home.

Oh yeah, you only have 1/5th the number of combinations if you make it at home.

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**36**DVD Talk Godfather

**Re: Mathematicians, Is this even possible?**

The real question is if the pizza delivery man shows up to a 3 apartment building with no addresses on the doors and picks door #1... nevermind.

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andicus (03-01-20)

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**42**Moderator

**Re: Mathematicians, Is this even possible?**

It is a minor semantic quibble, but I submit again that the question poses, "how many combination of number of toppings. There is necessarily needs to be a topping given the list provided. I understand you can order a plain cheese pizza in real life, but not here. More generally, this type of question is usually presented with examples where a choice is required. Pick x number of cards out of a deck, or what are number of combinations in lottery.

Either way, your were correct. Also interesting how you approach from a binary standpoint.

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**44**DVD Talk Legend

**Re: Mathematicians, Is this even possible?**

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.

Savages.

And 8x pepperoni sounds like a challenge. Accepted.

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