Dear Uncle Colin,

There are three of us, but only two pizzas - one with a diameter of 30cm and the other with a diameter of 24cm, each split into eight. How can we make sure each of us gets the same area of pizza ((Yes, we have two-dimensional pizzas. What of it?))?

- Pizza Is Not Exactly A Priesthood, People - Let’s Eat!

Hi, PINEAPPLE, and thanks for your message!

Let’s see what we’ve got here: a large pizza with area of $900\pi$ square centimetres, and a smaller pizza with area of $576\pi$. Those are in the ratio of 25:16, so we’ll say we have eight large slices with area 25 units and eight small slices with area of 16. Our total area is 328 units – so each of you needs to get a little over 109 units.

Clearly, we’re not going to get that exactly (our slices have integer areas), but how close can we get?

If someone had half of the large pizza, they would have 100 units; if the others split the remaining slices, they’d have 114 each. That’s a decent first effort.

If they swapped one of their large pieces for two smaller pieces, they would have 107; the person they swapped with would have 107, and the other 114.

So far:

Person A: 3 large, 2 small (75 + 32 = 107)
Person B: 3 large, 2 small (107)
Person C: 2 large, 4 small (50 + 64 = 114)

I don’t think we can do any better than this without splitting a slice! And since A and B are only about an eighth of a small slice down, I’d say this is good enough (and person C can tip the delivery driver).

Alternatively, starting from the 100-114-114 split, if each of the 114s cut a quarter off of a 16-slice and gave it to the other, it would be a 108-110-110 split. It depends on how fiddly you want to get with the cutting!

Hope that helps!

- Uncle Colin