BRAINTEASER about food rations, time, and number of people involved.

April 12, 2010 12:22 AM

One day at noontime six children became lost in a cave. Fortunately they had just enough food to feed themselves for four days. Unfortunatley, at noon on the next day they met another group of lost children who had no food but with whom they shared their rations equally. Fortunately, they all had just enought food to last them until they were all rescued at noon two days after their groups joined. How many children were in that second group?

Thanks, everyone!

posted by penguingrl to Education (23 answers total)

They had 24 daily rations to start with. They ate 6 during the first day, leaving 18. They met 3 more lost children, and the nine of them ate all 18 rations in the next two days.
posted by roofus at 12:27 AM on April 12, 2010

Wouldn't you need to know the minimum amount of food that a kid could eat and get by on? Also, are there any bears in the cave? That makes a huge difference.
posted by iamkimiam at 12:28 AM on April 12, 2010 [4 favorites]

Okay, so they start out with 6*4 rations. I assume they ate one ration between when they got lost and "noon the next day"

So they are left with 6*3 = 18 rations, which they finished in two days. So that's 18/2 = 9 kids. So there were three kids in the group.
posted by delmoi at 12:28 AM on April 12, 2010

To start they had 6 kids x 4 days of rations = 24 rations
After 1 day they'd all eaten 1 ration, presumably, so 24-6=18 rations remaining.
Then they met up with X number of kids such that 6 + x is half of 18 (because 18 rations last them 2 days).
If x=3, then 6+3 = 9, and 9*2=18.

So 3 kids are in the second group.
posted by EndsOfInvention at 12:30 AM on April 12, 2010

Also trying to imagine a real world scenario where you'd know how much food was had, but not how many people were involved. And having to work it backwards. You'd think counting heads would be the easy way to go!
posted by iamkimiam at 12:31 AM on April 12, 2010

Six kids need 24 daily rations for four days. (6x4=24). On the second day, 18 rations remain (24-6=18). They need two more days of food, at that point. They have 18 rations. 9 kids can eat 18 rations in two days. So 3 more kids were in the second group.

On preview, already answered, twice.
posted by The Potate at 12:35 AM on April 12, 2010

Three times. Sorry.
posted by The Potate at 12:36 AM on April 12, 2010

And I agree that no bears were accounted for in this exercise. Replace "rations" with "beanplates" and you're almost set.
posted by The Potate at 12:38 AM on April 12, 2010

Response by poster: Thanks, everyone! And no, it is not homework! :)
posted by penguingrl at 12:42 AM on April 12, 2010

Response by poster: I am just having fun with a few brainteasers and some are stumping me! Here is another one:

You are given two glasses. One holds exactly four ounces of liquid. The other holds exactly nine ounces. Using only these two glasses, but as much water as you want, how could you measure out EXACTLY (no "fill it half way" or "draw a little line on the glass" suggestions) six ounces of water with the least possible amount of effort? Hint: It should take no more than eight steps.
posted by penguingrl at 12:43 AM on April 12, 2010

Isn't that the problem from that Bruce Willis movie with a bomb in the park?
posted by taff at 12:47 AM on April 12, 2010

Oooh, I got this one! If the glasses are the same shape, put the 4 ounce next to the 9 ounce. Drink the nine ounce down so that it's the same water level as the four ounce. Now drink half the four ounce and dump the other half into the 9 ounce glass containing only 4 ounces of water!
posted by iamkimiam at 12:51 AM on April 12, 2010 [1 favorite]

Fill up the 9oz bottle, then ask the 4oz bottle how much the 9oz glass of water would tell me it contained if I were to ask it.
posted by fleacircus at 12:57 AM on April 12, 2010

Fill 9
Fill 4 with 9
Pour out 4
Fill 4 with 9(5)
Pour out 4
Pour 9(1) -> 4
Fill 9
Pour 9-> 4 (1)
9 now has 6 oz in it.
posted by one_bean at 1:01 AM on April 12, 2010 [1 favorite]

I think 'drink half of four oz' is similar to 'fill half way', iamk.

Do you have a third container? If so, first pour on small glass full into the other container, Then fill the small container from the large one twice and toss that water out. Pour the one oz left in with the other four ounces. Repeat step two.

If you have to get the six ounces the large glass I haven't a clue.
posted by Some1 at 1:04 AM on April 12, 2010

Response by poster: Some1, you are awesome! Thank you! I am making up a book of brainteasers for a friend and found a list from a class syllabus from an old professor, however, I never saved the answers. Thank you for helping me create a great book! Here's are the last two (unrelated to one another):

1) Jason and Jennifer each want to but themselves a pizza. Jason needs 10 more dollars to buy his pizza. Jennifer needs only one more dollar to buy her pizza. They decide to pool their resources to buy one pizza to share but they still do not have enough. Neither has any change; we are only dealing with whole dollars here. How much does a pizza cost?


2) A snail falls to the bottom of a very slippery well that is 9.5 feet deep. The snail is determined to get out, but the walls are so slippery that it takes the snail an entire day to climb up only three feet. Unfortunately, each night as he sleeps he slides two feet back down into the well. Despite the inevitable frustration of his condition, the snail persists and climbs out of the well as fast as he physically can. Assuming that the snail has to sleep every night, how many days will it take him to climb up out of the well?
posted by penguingrl at 1:18 AM on April 12, 2010 [1 favorite]

Wouldn't it be more fun to let your friend work out the answers or join MeFi and ask for themselves?
posted by taff at 1:36 AM on April 12, 2010 [1 favorite]

Response by poster: it's going to be a book that people can use as a game among a group of friends. i am making a collection in this book and these brain teasers are part of the questionnaires/trivia/dares for friends to do.
posted by penguingrl at 1:39 AM on April 12, 2010

$10. 8.
posted by fleacircus at 2:11 AM on April 12, 2010

2) It takes the snail seven days. On the morning of the seventh day, it's seven feet up the wall. It climbs three feet, which takes it over the edge of the well. No more sliding down.
posted by twirlypen at 2:17 AM on April 12, 2010

Yeah. Eight.
posted by twirlypen at 2:19 AM on April 12, 2010

The one with the glasses is the Puzzler from the Apr. 3 Car Talk show and was answered on the Apr. 10 show.
posted by DevilsAdvocate at 4:30 AM on April 12, 2010

penguingrl: Some1, you are awesome!


Well, yes. Yes, I am, but one_bean's solution works too and is a lot more elegant.
posted by Some1 at 4:38 AM on April 12, 2010