Saturday, August 8, 2009

A Common Thread

Read the following four logic puzzles and tell me what they all have in common.

Milky Water
Your are given two glasses, one containing exactly 50 tablespoons of milk, the other containing exactly 50 tablespoons of water. You take one tablespoon of out of the milk glass and mix it with the water. You then take one tablespoon of the water/milk mixture and mix it into the pure milk to obtain a milk/water mixture. Are you left with more water in the milk/water mixture or more milk in the water/milk mixture?

Four to Five
Make a word ladder starting with FOUR and ending with FIVE. (Every step in a word ladder differs by only one letter from the previous step, but each step must be an English word. You may add a letter, remove a letter, or change a letter, but the words from one step to the next must differ by only one letter.)

Clock Face
A clock face has the same symbol for all twelve hours, and both hands are exactly the same length (there is no second hand, only an hour hand and a minute hand). The clock stands opposite to a mirror. At what time between 6 and 7 o'clock will the time read exactly the same on the clock as in the mirror?

Ravens and Writing Desks
Why is a raven like a writing desk?

Before you answer something very general like "they're all word problems" or "they're all logic puzzles," I'll tell you that the common thread that I have in mind is something very specific. I'll have the answer to the four puzzles and what they have in common in an upcoming post.


Anonymous said...

They have no answers?
This is really a stab in the dark though beacause I'm pretty sure three out of the four (and sort of the fourth) do...

Bill the Lizard said...

Two of the four have definite answers that you can calculate. One has more than one answer. The last one didn't have an answer when it was first posed, but several answers were provided later. Good guess, though, considering the nature of the fourth riddle.

Tyler Breisacher said...

There's a certain feeling of "symmetry" to the milk/water one and the clock one, but I wouldn't necessarily say the same about the other two. Hm...

Bill the Lizard said...

Symmetry is definitely key to solving the clock face puzzle. It plays into the milk/water puzzle, but to a lesser degree. You don't really need to be thinking about symmetry to solve that one, but once you know the answer, it should be clear how symmetry is involved.

However, symmetry is not the common thread that links all four problems.

Anonymous said...

I've got the answer, but I'll keep it to myself until you want to share it.

I was happily finding solutions in the expectation that that's where the similarity would be, but then the last one prevented that. That one tipped me off though, because I happen to already know where it came from. I had to look up the others to verify I was right.

Very clever. ;)

Bill the Lizard said...

That was fast! I was hoping this might last a couple of days, but I've already written up the full solution, just in case someone solved it more quickly. I'll post it tomorrow (after I've proofread it a few more times).

By the way, I appreciate you not spoiling it for everyone else, while at the same time giving me just enough information to confirm that you have the right answer. Where the fourth puzzle comes from is a very good clue. :)

Thomas Guest said...

I certainly recognise the final one. So you're *that* Bill the lizard!

Here's another clock puzzle I wrote about.

Bill the Lizard said...

Thomas Guest,
Another subtle clue! :)

Also, that's an excellent article you linked to. Thanks for sharing. You just picked up a new subscriber.

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