I'm a bit confused on why we add 5 specifically. At 1:46, we added 5 to 16 slices making it 21 slices. How will this work in all cases, please? i.e. we can add 2 instead of 5 to the equation resulting in 18 slices and it would still give us the answer of 3 pizzas.

I think a possible explanation of the magic number 5 could be the following: When you need 7 slices, 7 mod 6 = 1...1 extra slice, so will need to order 1 more pizza to cover this 1 extra slice. When you need 8 slices, 8 mod 6 = 1...2 extra slice so will need to order 1 more pizza When you need 9 slices, 9 mod 6 = 1...3 extra slices so will need to order 1 more pizza When you need 10 slices, 10 mod 6 = 1...4 extra slices so will need to order 1 more pizza When you need 11 slices, 11 mod 6 = 1...5 <<<Magic number 5, & 5 extra slices so will need to order 1 more pizza When you need 12 slices, 12 mod 6 = 2...0 So the reminder of 6 will always be 1,2,3,4,5. It means if we add this largest mod (number 5) to our total needed slices, it will ensure we order 1 more pizza to cover the extra slices. So it will become: 7 slices +5 slices = 12 slices/6= 2 pizzas 8 slices +5 slices = 13 slices/6=2 Pizzas ..... 11 slices+5 slices=16/6=2 pizzas 12 slices+5 slices = 17/6=2 pizzas

Because we are using floor division we need to ensure that the number is always higher than the number of pizzas needed, if say we needed 8 slices and we just added 2, the number would be 10 and when dividing it would still return 1 pizza, by adding 5 we ensure we always go above 12. We don’t add 6 as that would be a whole other pizza, and if we actually had exactly the right number of people for whole pizzas, adding 5 would ensure we don’t order one pizza too many.