Soda Mixing Problem (revisited)

I posted a problem back in December that I never got back to answering. Sorry about that. The problem statement was:

Two jars contain an equal volume of soda. One contains Sprite, the other Coca Cola. You take a small amount of Coca Cola from the Coca Cola jar and add it to the Sprite jar. After uniformly mixing this concoction, you take a small amount out and put it back in the Coca Cola jar, restoring both jars to their original volumes. After having done this, is there more Coca Cola in the Sprite jar or more Sprite in the Coca Cola jar? Or, are they equally contaminated?

I have had the worked out solution for a while, just haven’t posted it until now. I’m relatively new with , but I’ve typed up the solution here, if you want all the gory details .  And yes, Peekay, you got the right answer!

Who am I? (hint)

I posted the following problem back on December 3. I thought I’d post the solution, but then I decided maybe to just give you a hint. I’ve emboldened each true statement. The other statement in each pair is false. I did a lot of trial and error, making lists of numbers and crossing things off, narrowing it down. I didn’t have a great strategy, so see if you can do better. Can you figure out the number now?

There are five true and five false statements about the secret number. Each pair of statements contains one true and one false statement. Find the trues, find the falses, and find the number.

1a. I have 2 digits
1b. I am even

2a. I contain a “7”
2b. I am prime

3a. I am the product of two consecutive odd integers
3b. I am one more than a perfect square

4a. I am divisible by 11
4b. I am one more than a perfect cube

5a. I am a perfect square
5b. I have 3 digits

Awesome Illusion

Which square is darker, A, or B?

(originally found here) (go here for the answer)

Soda Mixing Problem

Here’s a good puzzle for you!

Two jars contain an equal volume of soda. One contains Sprite, the other Coca Cola. You take a small amount of Coca Cola from the Coca Cola jar and add it to the Sprite jar. After uniformly mixing this concoction, you take a small amount out and put it back in the Coca Cola jar, restoring both jars to their original volumes. After having done this, is there more Coca Cola in the Sprite jar or more Sprite in the Coca Cola jar? Or, are they equally contaminated?

This problem has been stated in many different ways, with various liquids. I’ve phrased it in my own way. If you search around the internet, you can find the solution. But I want you to think it through. Give an answer and see if you can justify it! (I’ll post my solution later.)

Elegant Puzzles on TED

Another great TED talk, this one on the art of making puzzles. Bon appetit!

Who Am I?

I’m reposting this great puzzle, found originally at The Math Less Traveled blog. Enjoy!

 

There are five true and five false statements about the secret number. Each pair of statements contains one true and one false statement. Find the trues, find the falses, and find the number.

1a. I have 2 digits
1b. I am even

2a. I contain a “7”
2b. I am prime

3a. I am the product of two consecutive odd integers
3b. I am one more than a perfect square

4a. I am divisible by 11
4b. I am one more than a perfect cube

5a. I am a perfect square
5b. I have 3 digits

One of These is not Like the Others

What a delightful puzzle! Can you figure it out?

Thanks to The Math Less Traveled blog for this gem!

 

Einstein’s Puzzle (Answer)

Okay, don’t read any further unless you’ve already tried the puzzle. It’s a classic logic puzzle and can be solved by the standard grid-technique, like commentors suggested. I did the same thing, and I got this answer:

The German owns the fish.

Did you get that too? Here’s the thing: It’s technically not correct, according to a few sources I found. Some people say the correct answer to this problem is “there’s not enough information; the fish isn’t even mentioned in the listed facts.” I’m not sure what I think, but it gives some food for thought. Consider the following new problem and you’ll see why:

Who is the American?

(Fact 1) Winston and Paul are of two different nationalities

(Fact 2) Paul is Canadian.

What do you think? Would you say “Winston” or would you say “Winston could be anything (except Canadian) given the facts”? If you say “Winston” then you’re actually assuming a third fact: One of them is an American.

In the case of Einstein’s Puzzle, we technically need a 16th fact: One of them owns a fish.

So what do you think? Those of us who solved the puzzle in the classic logic-problem grid-solution way simply assumed that fact and got on with our lives. But what do you think? Do you think we can assume that someone owns the fish even though it’s technically not a “fact?” It’s an interesting issue–perhaps just a linguistic one. Let me know what you think.

Einstein’s Puzzle

Thanks to Drew for pointing me to this fun logic puzzle.

Supposedly Einstein proposed this puzzle and it’s often referred to as “Einstein’s Challenge.” The question is, “Who Own’s the Fish?” And here’s the information. Go ahead and try it. And by presenting this puzzle, I am NOT advocating smoking or drinking, I merely wanted to quote the puzzle as it’s classically written.

Here’s what we know:

1. There are five houses in five different colors.
2. In each house lives a person of a different nationality.
3. These five owners drink a certain beverage, smoke a certain brand of cigarette and keep a certain pet.
4. No owners have the same pet, smoke the same brand of cigarette or drink the same drink.

Here are the clues:

1. The Brit lives in the red house.
2. The Swede keeps dogs as pets.
3. The Dane drinks tea.
4. The green house is on the immediate left of the white house.
5. The green house owner drinks coffee.
6. The person who smokes Pall Mall rears birds.
7. The owner of the yellow house smokes Dunhills.
8. The man living in the house right in the center drinks milk.
9. The Norwegian lives in the first house.
10. The man who smokes Blends lives next to the one who keeps cats.
11. The man who keeps horses lives next to the man who smokes Dunhills.
12. The owner who smokes Bluemasters drinks beer.
13. The German smokes Princes.
14. The Norwegian lives next to the blue house.
15. The man who smokes Blends has a neighbour who drinks water.

Again, the question is: WHO OWNS THE FISH?

The fact that Einstein proposed the problem is urban legend. I’m not sure why it’s named for him. Also, most sources say something like “2% of people who try this problem get it correct,” which is a completely made up statistic, as far as I know.

 I didn’t get it right, if that’s a comfort to you . So see if you can do better than me!