# the dining mongers problem

Greg McCarroll greg at mccarroll.org.uk
Thu Oct 12 21:57:49 BST 2006

```So, I'm having some friends around tomorrow night so I asked them
what they'd
like to eat, their 'leader' suggested Pizza so this reminded of a
social problem
that might be interesting from a computational or algorithmic point
of view - I
really don't know as I haven't attempted it yet, anyway here it is.

You have N mongers coming around.

They all want to be able to have H (hunger) pieces each

Each pizza has S slices

You want to order the minimum number of pizza's, so i guess thats
whatever ceil((N*H)/S)

You ask them all for 3 toppings they want and ask them for 3 toppings
they cannot eat pizza with, e.g. they are fussy like me (sweetcorn)
or they maybe are allergic to seafood. (I guess you could generalise
both these numbers).

There is a set menu of toppings (although i'm guessing this could
be ignored for the union of all the topics they want).

How can you please the mongers the most?

There is a basic solution that makes everyone not unhappy, of ordering
ceil((N*H)/s) pizza's with no toppings on any of them, i.e. bread ;-)

Anyway I don't know if this will turn out to be an interesting
problem or
not, but I thought I might as well share it.

Greg

p.s. full solutions that support data entry for N people will be
tested ;-)
p.p.s. i'm guessing some of the interest might come out of how some
toppings
spoil it for others.
p.p.p.s. and of course this can be brute forced.
```