### Brain Teasers

# How Many Campers?

Math
Math brain teasers require computations to solve.

Camp Pineveiw's cook, Margaret Johnson, was just about to begin preparing the picnic lunch for all the campers. She already knew she needed to fill 55 bowls of the same size and capacity with the same amount of food. When she was done, she decided to read the guidelines for the picnic, just out of curiosity. The guidelines said:

1. Every camper gets their own bowl of soup.

2. Every two campers will get one bowl of spaghetti to share.

3. Every three campers will get one bowl of salad to share.

4. All campers are required to have their own helping of salad, spaghetti, and soup.

After some rapid calculations, Margaret was able to figure out how many campers were going to the picnic. Can you?

1. Every camper gets their own bowl of soup.

2. Every two campers will get one bowl of spaghetti to share.

3. Every three campers will get one bowl of salad to share.

4. All campers are required to have their own helping of salad, spaghetti, and soup.

After some rapid calculations, Margaret was able to figure out how many campers were going to the picnic. Can you?

### Hint

If there were only six campers, there would be six bowls of soup, three bowls of spaghetti, and two bowls of salad.### Answer

30 campers.Hide Hint Show Hint Hide Answer Show Answer

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## Comments

An easy way to think about it: each camper gets 1 + 1/2 + 1/3 bowls, or 1-5/6, or 11/6. x times 11/6 = 55; 55 times 6/11 = x = 30.

I solved it by doing

x + x/2 + x/3 = 55

which leads to

3x + 1,5x + x = 165

that's

5,5x = 165

Easy as pie!

x + x/2 + x/3 = 55

which leads to

3x + 1,5x + x = 165

that's

5,5x = 165

Easy as pie!

I don't understand rule #4. "their own helping" seems to imply the portions are to be served separately, but the description makes it clear that all bowls are filled with the same amount of food, and each person is only rationed 1/2 bowl of spaghetti, and 1/3 bowl of salad. I think if you remove rule #4 what is being asked becomes clearer.

A fun teaser . All #4 means is that the case is simplified... everybody has every food prepared for them.

A pretty goon one, you have to think at first at the calculator is usually necassary, but it was fun!

i just kept goin up by numbers divisible by 2 and 3 and i got it right!

good one!!

Math is not my favorite thing, but this one was fun. Thanks for posting.

I got so hungry reading the quiz that I ate two shares of food. Does that mean the answer is only 29

wow my school is called Pine View and there's a Margeret Johnson

Once I got my brain calculater going, it was pretty easy. But still a great math riddle.

That was good! When I saw that the hint for 6 people made 11 bowls, it was easy to just multiply 6 by 5 (since 11x5=55), and there's your answer. Nice teaser!

Piece o' cake. but very fun!

55/1.8333333=30

55/1.8333333=30

Cool, finally a teaser for us math fans.

Honestly didn't get the answer from the clues. Checked the hint and saw that 6 campers need 11 bowls. The cook prepared 55 bowls therefore 6X5= the solution.

Good teaser!

Good teaser!

tat was easy ! decided to ignore #4 since i didnt understand tat one .. love camping but we usually have gourmet cuisine and no sharing bowls ;-)

--I GOT LOST BETWEEN THE SPAGHETTI AND THE SALAD.....

Sorry I got food craving too, so archer and I may have messed up the answer

I love math problems.

I guessed the answer, checked it, and got it right the first time!!!

I guessed the answer, checked it, and got it right the first time!!!

At first I did not understand and keep getting the wrong answers. If I didn't read the hint, I would not have figured out that I would first use proportion. It was fun though

OK teaser, but just a very basic algebra question. Not sure why this is one of the most popular teasers.

trial & error

C = # of campers = unknown

B = # of bowls = 55

B = C + 1/2C + 1/3C

55 = C + 1/2C + 1/3C

6(55) = 6C + 3C + 2C

330 = 11C

30 = C

Great puzzle!

B = # of bowls = 55

B = C + 1/2C + 1/3C

55 = C + 1/2C + 1/3C

6(55) = 6C + 3C + 2C

330 = 11C

30 = C

Great puzzle!

A good challenge, written in a fun context. Thanks - that's why it's one of the more popular ones!

Jun 11, 2011

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I like camping and I like food. Beyond that, I was lost. Have a simply wonderful day friends!

Quite simple to figure out, but quite enjoyable.

Still easy.

Pretty easy to get, I literally got it in 3 minutes....

simple, but fune

My eyes glazed over and my head began to spin.......and that was before I had finished reading the entire teaser.

....but, I noticed that Pineview was misspelled.

I had forgotten about this one. It is a great teaser, fairly easy, but well done.

I hate math, so I did not even try this one. I love catmom's comment, and it sounds like she did not try this one either. Funny!

Not usually a math fan, but I gave this one a try and lo and behold I finally got it.

That was a lot of fun! I got lost in the math as I have a lot of trouble turning a word problem into an equation, but I fought my way through and figured out the answer!

Enjoyed this fun, entertaining and challenging teaser; it took a little while but I got it. I did not think of turning it into an equation just testing numbers divisible by 2 and 3 starting with 12 using the hint as a reference.

This is a terrific puzzle. It's an excellent exercise in translating language into mathematics. For math people, it was quite easy. But not everyone does fractional algebra in their heads, nor do they want to! So, the puzzle could also be solved using logic and a bit of trial and error. Fun for all ages!

Let x = the number of campers.

x + x/2 + x/3 = 55

6x + 6(x/2) + 6(x/3) = 6(55)

6x + 3x + 2x = 6(55)

11x = 330

x = 330/11

x = 30

Therefore, 30 campers will have/share:

30 (=x) bowls of soup (every camper gets their own bowl of soup), +

15 (=x/2 =30/2) bowls of spaghetti (every two campers will get one bowl of spaghetti to share), +

10 (=x/3 =30/3) bowls of salad (every three campers will get one bowl of salad to share) =

----

55 bowls in total.

Great teaser!

x + x/2 + x/3 = 55

6x + 6(x/2) + 6(x/3) = 6(55)

6x + 3x + 2x = 6(55)

11x = 330

x = 330/11

x = 30

Therefore, 30 campers will have/share:

30 (=x) bowls of soup (every camper gets their own bowl of soup), +

15 (=x/2 =30/2) bowls of spaghetti (every two campers will get one bowl of spaghetti to share), +

10 (=x/3 =30/3) bowls of salad (every three campers will get one bowl of salad to share) =

----

55 bowls in total.

Great teaser!

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