A Little Pizza Problem

by golbguru on September 5, 2007

pizza closeupHere is a 5-minute pizza workout for you.

A quaint little pizzeria sells the following specialty pizzas at the prices mentioned:

  • 9″ pizza: $8.00
  • 13″ pizza: $12.00
  • 16″ pizza: $15.00
  • 19″ pizza: $26.00

You have been given $26 for buying some pizzas and you are asked to “make the best of it”. If you get some change back from your order, it is yours to keep.

Which pizzas will you order?

Note: “make the best of it” is a little open ended requirement, but it will be more fun that way.

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{ 31 comments… read them below or add one }

1 Lynnae @ Being Frugal 09.05.07 at 2:17 pm

Well, if I wanted the most pizza for my money, I’d order the 19″ pizza. But for the best experience, I’d probably order a 16″ pizza that my husband and I like, a 9″ pepperoni pizza for the kids, and we’d use the change to send the kids off to the video games, so we could have a quiet moment together. Then we’d use the leftovers from the 16″ pizza for lunch the next day. :)

2 Joseph 09.05.07 at 2:31 pm

I’d buy the 9” pie for 8 dollars, and keep the change.

This was ‘I’m making the most of it’ (financially.)

3 DG 09.05.07 at 3:03 pm

Mathematically speaking the best deal is the 16″.

The costs are as follows
9″: $0.126 / sq. in.
13″: $0.090 / sq. in.
16″: $0.075 / sq. in.
19″: $0.092 / sq. in.

So Joe, I disagree that you are making the most of it, unless you don’t like pizza. Why not buy the 16″ one and use it as leftovers to replace a couple of meals you would otherwise be spending money on.

Pizza is fairly economical, and you’d be hard pressed to find replacement foods that would cost you less than the additional $7 of pizza. The 16″ pizza is more than 3 times bigger than the 9″. Pretty good for $7 more.

4 Mike 09.05.07 at 3:03 pm

I’d get the 16″ and keep the change, unless it wasn’t enough pizza for whoever I was feeding, in which case I would throw in another dollar and get a second 16″

The 16″ gives more pizza per dollar, and like what was mentioned above, you can always have leftover pizza another time.

5 Exick 09.05.07 at 3:19 pm

Here’s a breakdown of the 9 ways you can go with square inches of pizza per dollar and the change you receive.

1 pizza
1 19″: 43.6/$1 + $0
1 16″: 53.6/$1 + $11
1 13″: 44.2/$1 + $14
1 9″: 31.8/$1 + $18

2 pizzas
1 16″,1 9″: 46.0/$1 + $3
2 13″: 44.2/$1 + $2
1 13″,1 9″: 39.3/$1 + $6
2 9″: 31.8/$1 + $10

3 pizzas
3 9″: 31.8/$1 + $2

6 DG 09.05.07 at 3:36 pm


I agree with everything you did except I think you used the diameter and not the radius when calculating the areas.

Unless I’m mistaken, pizza joints usually give you the diameter when talking size.

7 Rashers Tierney 09.05.07 at 3:46 pm

It has been scientifically proven by, er, scientists that when pizza is ordered for the office, women will only take one piece and then hang back, wait to see what happens and possibly take a second one when it’s cold and no-one’s watching. Men will dig in and eat as much as their little paws can throw down their throats. Therefore the correct answer if you are a woman is: the 19″ pizza.

8 Laura 09.05.07 at 4:12 pm

Two 13″ pizzas are the most amount of pizza you can buy for $26 or less.

But that is too obvious so I’m probably wrong. ;)

9 Julian 09.05.07 at 4:34 pm

Each pizza, in terms of $ per square inch:
9″ $0.126
13″ $0.090
16″ $0.075
19″ $0.092

So assuming that “making the best of it” meant getting the most pizza possible, one should get a 9″ and a 16″ (264.58in^2) for $23: $0.087 per square inch.

And give a $3 tip to the delivery person.

Yum. Pizza.

10 Adam 09.05.07 at 4:51 pm

The “make the best of it” is an interesting little addition to this problem.

According to American Sports Data (http://www.americansportsdata.com/obesitystats.asp), in 2004 63% of Americans were considered to be overweight, and 31% were considered to be obese.

For the purposes of this problem, let’s bet with the odds and assume the “you” in this question is both American, and overweight. Furthermore, let’s assume that we’re talking about regular pizza (i.e. this isn’t some miracle pizza that causes you to lose weight). Under this assumption, according to Nutritiondata.com (http://www.nutritiondata.com/facts-C00001-01c22QQ.html), a slice of 14″, cheese-only, regular crust pizza contains a whooping 22% of a 2000-calorie dieter’s recommended saturated fat intake. For simplicity’s sake, let’s assume that this value holds true for a 13″ pizza, the size used in this problem (if this assumption is a problem for you, imagine you added another topping to the 13″ pizza).

Therefore, if you consider that a typical overweight American would consume no less than one half of a 13″ pizza, equating to 88% of one’s recommended daily fat intake, and if you consider that it is highly probable that this number is likely to be only one of multiple, similar high fat meals to be consumed during the course of the day, then my recommendation would be simple:

Buy a $4 salad, and put the $22 remaining towards a gym membership.

11 FrugalTrader 09.05.07 at 5:20 pm

All depends on the number of people i’m trying to feed. No point saving money if there’s not enough food to feed the guests!

12 Brandon 09.05.07 at 8:41 pm

I’d save the money and eat a sandwich. LOL.

13 MoneyNing 09.05.07 at 9:37 pm

I would save the money and buy something else for less. But if I had to choose one, I will do what Joeseph did (buy the 9″ and keep the change!)

14 The Financial Blogger 09.06.07 at 3:07 am

I would say 2 13″ and take the extra $2 for extra bacon! You always get the most of it with extra stuff!

15 plonkee 09.06.07 at 4:17 am

You get the most pizza for your money with the 19″. I’d be tempted to get the 9″ and keep the change though.

16 Stephen Ward 09.06.07 at 5:28 am

If by “make the best of it,” you mean get the most volume of pizza possible for $26, then you’d get one 19″ pizza (283.52 square inches).

If by “make the best of it,” you mean get the most pizza per dollar, then you’d get one 15″ and one 8″ (264.67 square inches at a rate of 11.51 square inches per dollar).

If you really want the best deal, you’d ditch the pizzeria, go down to your local grocery club, buy in bulk, and cook them at home. My local Sam’s Club, for example, sells Digiorno three-packs for $11.88. For about $24, then, you could get six full-size pizzas, easily a better deal than anything the pizzeria offers, not too much added hassle, and plenty of leftovers. ;)

17 Exick 09.06.07 at 6:48 am

Yeah, I’m pretty sure I did, DG. Oops. So everyone can divide those areas/dollar by 4 and pretend I’m not an idiot.

18 Debbie 09.06.07 at 6:54 am

Yep, the most pizza you can get with $26 is one 19-inch pizza (284 sq in). This will cost the whole $26.

The best bargain is the 16-inch pizza, but you can’t quite afford two.

You can get close to as much pizza as you get from the 19-inch one by either getting two 13-inch pizzas (265 sq in) for $24 or a 9-inch and a 16-inch (also 265 sq in) for $23. So if most people wanted one set of toppings but a few people wanted another set, I’d get the 9-inch plus 16-inch.

Otherwise, I’d go with the one big pizza, because it also has the least crust per square inch and people tend to like the crust less than the other part. (You can make it half one set of toppings and half another.)

For those of you running home or running off with half the money, yeesh! This is SOMEONE ELSE’s money, not yours. And they have asked you to go to a certain pizzaria, not wherever you want. And they want you to quickly pick something up, not go home and start cooking. I think it’s clear that what’s meant by do the best you can is to get the most pizza you can, from the place requested, with the money you are given. What you would do with your own money for your own lunch is not what this question is about. (Although giving that answer in addition to the answer requested as Lynnae and Stephen Ward did is always fun.)

Lesson: never trust other people with your money, if at all possible. Except Mike is totally awesome for throwing in another dollar, but wouldn’t you need to throw in another $4? And the Financial Blogger is totally awesome for giving us extra bacon!

19 Steve Austin 09.06.07 at 7:44 am

I liked Debbie’s comments on toppings and less crust per sq.in. for larger pizzas.

My answer(s):

* What about the toppings? Don’t they cost extra? If so, I recommend the 16″ and jack it up with $11 in high-end toppings.

* If no toppings available (or they don’t cost extra), remember that everything is negotiable. Show up and observe the pizzeria operation for a few minutes. See if there are any pizzas sitting on a rack that appear not to be moving. Someone may have failed to pick up an order.

To the pizzeria manager: “I want a 13 in. and a 16 in. pizza, but I only have $26. Would you sell me one of those unclaimed 13 in. or 16 in. pizzas on your rack there at a $1 discount?”

20 Minimum Wage 09.06.07 at 8:57 am

The 16″ pizza is clearly the best value. I’d buy that and keep the change.

21 golbguru 09.08.07 at 3:41 am

It’s really interesting to see some lateral thinking here. Thanks for the input. I will run a few numbers and make a quick post about it either today or tomorrow.

Looking back, I could have made it a bit more interesting by offering a 18″ pizza for 26 bucks instead of the 19″ pizza.

22 agressive saver 09.08.07 at 5:34 am

i see a lot of posts on people calculating the unit prices (per square inch) of the pizzas, which is what i would do normally, but you can save a bit of time on the calculation by ignoring the actual formula for computing the area of a circle (a=pi * r^2) by eliminating the pi — it’s just a constant after all and the price is merely related directly to the square of the radius of the pie. it may help if you’re actually in line at the pizza parlor and trying to do some quick math in your head.

23 I buy and sell 09.08.07 at 7:07 am

I would invest this huge amount of money into some shares and after 10 years or so (hopefully) buy 10 pizzas.

24 Minimum Wage 09.09.07 at 12:25 pm

Eliminate the pie and keep the money? (actually, i did eliminate (ignore, actually) the pi, since it was completely unnecessary to calculating the best deal.)

25 Anup Kumar Agarwal 04.18.08 at 10:01 pm

let the height of the pizza be x inch and the pizza be a circular one.
9″….$1=31.82x cubic inch
13″…$1=44.26x cubic inch
16″…$1=53.63x cubic inch
19″…$1=43.63x cubic inch
so the best buy is 13″ pizza
so, i’ll definately buy 2 pizzas of 13″ for $24 and save $2. (here i’ve considered 9″, 13″ etc. as radius, if it were diametre than also my decision would be the same)

26 Camera warehouse 07.31.12 at 9:55 am

i like the way of thinking of anup, its what i thought to do. buy 2 pizza of 13″.

27 Mini Vibrator 10.30.12 at 10:34 pm

I always bus 16? pizza: $15.00 pizza,because in mathematically this pizza is provide big quantity and less price in compare other.

28 Cheap dedicated server 02.18.13 at 8:39 am

I would go for the 16and 9 inch I think that is the best bang for the amount of money and the left over would be tip.

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