How is "Big Pizza", the way you eat it, prime numbers, and the biggest act of corporate collusion the century has ever seen all connected? I'm about to take you on a journey, my friend.

- Sign my petition and join the fight against "Big Pizza" (you're already a soldier but you might be on the wrong side).
- Start cutting your pizza in 12 slices.
- Check out the math that definitively
*proves*my argument.

We've all been there more times than we care to remember. Pizza math... How many slices do and therefore boxes of pizza do we need to achieve maximal group pizza euphoria?

But why is it that we *always* seem to just need that *one* more box to put us
over that threshold? We always just need that one or two more slices but we need
to get an entire additional box. *Every.**Dang.**Time.*

Is it just me? Or is there something fishy, dare I say *insidious* going on here?

Well it's not just me, and I'll come right out and say it:

"Big Pizza" knows that by putting 8 slices of pizza in a box they sell more pizza... it's basic

MATH!

"Big Pizza" isn't stupid. They know *all* about math. They probably had a team of
mathematicians work out the ideal number of slices per box that would maximize
profits! Do you think it's a coincidence that every major pizza chain (that I can
think of) uses 8 slices a box? If *that* is not unequivocal proof of corporate
collusion I don't know what is!

I'll spare you the math (for now), but here's how it breaks down how many boxes
you need. And before you get all uppity and say "well it depends on how big the
pizza is and how hungry the people are." I'll just tell you now: *it doesn't
matter*. And I'll prove it later.

Fine. I'll prove it now because I can feel your skepticism penetrating space and time and goading me on my couch as I write.

If you get a bigger pizza, people just want fewer slices, so you'd just be looking
at the table respectively. The point is that in aggregate, 8 slices a box
increases the overall number of boxes you need to buy because of how it *divides*
pizza slices among the eaters. People don't share slices unless they're freaks.

1 Slice/Person | 2 Slices/Person | 3 Slices/Person | 4 Slices/Person | 5 Slices/Person | |
---|---|---|---|---|---|

2 People | 1 | 1 | 1 | 1 | 2 |

3 People | 1 | 1 | 2 | 2 | 2 |

4 People | 1 | 1 | 2 | 2 | 3 |

5 People | 1 | 2 | 2 | 3 | 4 |

5 People | 1 | 2 | 3 | 3 | 4 |

6 People | 1 | 2 | 3 | 4 | 5 |

Let's look at how many boxes you *would* need if instead of cutting pizza `8`

slices it was cut into `12`

:

1 Slice/Person | 2 Slices/Person | 3 Slices/Person | 4 Slices/Person | 5 Slices/Person | |
---|---|---|---|---|---|

2 People | 1 | 1 | 1 | 1 | 1 |

3 People | 1 | 1 | 1 | 1 | 2 |

4 People | 1 | 1 | 1 | 2 | 2 |

5 People | 1 | 1 | 2 | 2 | 3 |

5 People | 1 | 1 | 2 | 2 | 3 |

6 People | 1 | 2 | 2 | 3 | 3 |

If you've been following along you'll see that the maximum number of boxes needed
in the worst-case scenario here are `3`

whereas with 8 slices a box it's `5`

.
Or to put it in common-speak:

8 slices lots of red. 12 slices not so lots of red.

Let `e`

equal the number of pizza eaters, `s`

equal the number of averages slices
per eater, & `p`

equal the number of slices of pizza per box:

`Number of Boxes Needed = (e * s) / p`

Now we all know that "Big Pizza" doesn't sell partial boxes, so of course, we need to use a ceiling function (or round up) to the next highest box to achieve the maximum pizza vibes we're going for:

`Number of Boxes Needed = ceiling((e * s) / p)`

The problem is this rounding up necessity. Enter highly composite numbers (anti-primes).

I won't get too much into the weeds here but basically, highly composite numbers are:

Positive integers with more divisors than any smaller positive integer.

In simple terms, they're numbers that are super friendly to dividing up neatly.
It's probably easier to just see it, so below is a list of the first 10 highly
composite numbers. And wouldn't you know it, what number is conspicuously
absent? And look what number happened to be *on* the list? 🤔🤔🤔

Number | How Many Numbers Evenly Divide It | The Numbers That Divide It |
---|---|---|

1 | 1 | 1 |

2 | 2 | 1, 2 |

4 | 3 | 1, 2, 4 |

6 | 4 | 1, 2, 3, 6 |

12 | 6 | 1, 2, 3, 4, 6, 12 |

24 | 8 | 1, 2, 3, 4, 6, 8, 12, 24 |

36 | 9 | 1, 2, 3, 4, 6, 9, 12, 18, 36 |

48 | 10 | 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 |

60 | 12 | 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 |

120 | 16 | 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 |

At this point, you might be thinking: "Well why not 6?" And I say to you: "Just
chill." I'm down with 6 too, so long as it's not 8. In all honestly "Big Pizza"
probably could've done us worse by choosing *7* as it's prime, but the logistics
of getting pizza cut nicely into 7 slices would've been an operational headache,
not to mention being **even more blatantly obvious than 8**.

"Big Pizza" has been getting fat on our extra pizza dough (that's right, I said
it) for far too long. Sign my petition and as a great man once said let's "*save*
the change we want to *spend elsewhere* in the world.

It's not hard, simply start the way you normally start cutting pizza and then modify it slightly:

- Slice your pizza right down the middle.
- Turn the pizza 90° and cut down the middle again.
- Now divide each 1/4 section into 3rds (I.e. rather than just one big cut down the center of each quarter, do 2 evenly spaced cuts.)