[rickjosh19]

The council is ordering pizza for their next meeting. There are 20 council members, 7 of whom are vegetarian. A committee of 3 will order 6 pizza from a pizza shop that has a special for a large pizza with up to 3 toppings. The shop offers 10 toppings.

The committee wants as much variety as possible in the toppings. They decide to order each topping exactly once and to have at least 1 topping on each pizza. Describe the different cases possible when distributing the toppings this way.

[Perito]

6 pizzas / 20 members = 0.3 pizza per member. If you have 7 vegitarians, you need at least 3 meatless pizzas (7 members * 0.3 pizzas/member = 2.1 pizzas). Since you don't know what the toppings are, I'm not sure what you do with this.

6 pizzas with 1 topping on each pizza means you use 6 toppings and have 4 toppings left over. You can have a) 2 pizzas with 3 toppings and 4 with only 1 topping, or you can have b) 1 pizza with 3 toppings and 2 pizzas with 2 toppings and 3 pizzas with only 1 topping, or you can have 4 pizzas with 2 toppings and 2 with only one topping.

[sarnian]

Hello rickjosh

When you share 6 pizza's with 20 people, that means 6/20 = 0,3 pizza per person maximal. As this does not work out with the number of possible toppings (3 per pizza max) you will have several angry politicians because they get less pizza (or a collection of some very small added slices) than their peers. And the distribution of pizza slices will be a total mess.

Besides that : will a vegetarian accept 1/3 of a pizza that has a meat topping on the remaining 2/3 only ? Does not sound very 'kosher'! Specially attention for the cheese cover of that pizza, as some vegetarians also refuse milk products.

I strongly suggest to give the town clerk a cheap calculator, so that he/she can calculate the extra cost for ordering 7 pizza's. Or collect some money to pay for the additional pizza. This will produce 21 slices of 1/3 pizza each, it will be easier to distribute and share, and keep the meeting more pleasantly. And the mayor can have the remaining 1/3 pizza to build-up some extra strength against the continuously infighting council members...

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There are 10 different toppings. If you buy 7 pizza's you have 7 x 3 toppings (of any type).
With 20 people that means that at least two people share the same topping.
As to the vegetarian toppings : I doubt that there are 3 or more different vegetarian toppings.
So I hold further calculations till that info becomes available... :)

[devil0101]

to rickjosh => bro if you are taking ilc mdm4u course. Can you email me at [email protected]. I need some help for the last 2 units.

[Perito]

Note the original posting date.

[bacardiONICE]

Hey there I was wondering if you did the mdm4u-B exam. If so do you remember anything about the exam? And also should I rely on the practice test? Thanks ;)