Slashdot Log In
Your Favorite Math/Logic Riddles?
Posted by
Cliff
on Sat Oct 15, 2005 11:35 PM
from the top-10-mind-twisters dept.
from the top-10-mind-twisters dept.
shma asks: "Whether you're involved in the Sciences, Mathematics, or Engineering, you undoubtedly enjoy finding simple solutions to seemingly difficult problems. I'm sure you all have a favorite mind-bender, and who better to share it with than the Slashdot community? Post your own problems and try to solve others. Just one request: If you have figured out the solution, link to it in a post, rather than write it out where anyone can see it." What brain benders tickle your fancy?
"Here's a sample to consider: You're in a dark room with 50 quarters, 18 of which are heads up. You are allowed to move around the coins or flip some or all of them, if you wish. Problem is, it's too dark to tell what you're moving or flipping (no, you can't figure it out by touch either). Your job is to split the coins into two groups, each of which has the same number of heads up coins. How do you accomplish this?"
This discussion has been archived.
No new comments can be posted.
The Fine Print: The following comments are owned by whoever posted them. We are not responsible for them in any way.
Soduku (Score:4, Interesting)
-B
Another online version (Score:5, Interesting)
Keeping my skills fresh (Score:4, Interesting)
The Answer.... (Score:5, Funny)
easy one (Score:5, Funny)
Re:easy one (Score:5, Interesting)
Re:easy one (Score:5, Informative)
a^0 = 1
b^0 = 1
c^0 = 1
1 != 2
So, I would submit that that might be true for all nonzero values of n.
Re:easy one (Score:5, Informative)
Re:0^0 (Score:5, Funny)
One possible solution: (Score:5, Funny)
Re:One possible solution: (Score:5, Interesting)
I was once a judge at a "Phyics Olympics" where there was one puzzle in which students had to figure out the wiring if a circuit consisting of a couple of light bulbs and a couple of switches. They were "supposed" to solve the puzzle by flipping the switches, noting what lights were on and off, and inferring the circuit.
One team took the apparatus apart and inspected the wiring.
I gave 'em full marks.
The head judge went spare.
Science is not a game, and there aren't any rules according to which you are "supposed" to solve the problem. Alexander the Great was demonstrating the practice of experimental science when he unravelled the Gordian knot, and Feyrabend was onto something when he said, "Anything goes."
Puzzles set by humans have more to do with communication between the puzzle-setter and the puzzle-solver than anything else. Some people even decry computer-generated puzzles because of this--they say that the pleasure they get from solving puzzles comes from the feeling of interaction with another mind.
Petals of the Rose (Score:5, Interesting)
Bill Gates is said to have solved the problem by memorizing the combinations first [borrett.id.au], the brute force approach.
It ones of those that requires a knack for seeing the simple things
Re:Petals of the Rose (Score:5, Funny)
Max: My teacher tells me beauty is on the inside.
Fletcher: That's just something ugly people say.
-- "Liar Liar"
Lightbulb problem (Score:5, Interesting)
- One room has three switches, labeled A, B, and C.
- Another room has three light bulbs, labeled 1, 2, and 3.
- Each switch is connected to one bulb, but you do not know which is connected to which.
- When inside either room, you cannot see the other room.
- You begin in the room with the switches and may turn the switches on and off in any way you choose.
- Once you leave the room with the switches, you may not reenter it. You may, however, go to the room with the light bulbs.
How can you determine which switch is connected to which light? Here is a hint [nicemice.net] and solution [nicemice.net].I like this problem because people are ordinarily good at logic have so much trouble with it. I once had the pleasure of meeting Donald Knuth and stumped him with this puzzle.
Re:Lightbulb problem (Score:5, Insightful)
Say for example all the bulbs are initially ON, and you flip two of the switches to what you think is on. Then when you flip one of them to what you think is "off" and wait a while, and go in to the room, you'll find two bulbs on, but you'll misidentify them because the one you thought you switched to "off" you actually turned "on". Not to mention they could be in mixed states initially..
Sticky Triangles (Score:5, Interesting)
If I give you 3 sticks, you can make one triangle. If I give you 2 more sticks (5), you can make 2 triangles. If I give you another stick (6), how can you make 4 triangles?
My all-time favorite logic puzzle (Score:5, Interesting)
But anyway, logic puzzles. This logic puzzle is excellent. I've had it up on my site (http://www.xkcd.com/blue_eyes.html [xkcd.com]), and after I got boingboing'ed I got a lot of email about it, so I've been able to tweak the wording to get rid of most of the confusing stuff, leaving only the logic. It's extremely subtle; I've never seen anything like it.
Here's the puzzle:
A group of people live on an island. They are all perfect logicians -- if a conclusion can be logically deduced, they will do it instantly. No one knows the color of their eyes. Every night at midnight, a ferry stops at the island. If anyone has figured out the color of their own eyes, they [must] leave the island that midnight.
On this island live 100 blue-eyed people, 100 brown-eyed people, and the Guru. The Guru has green eyes, and does not know her own eye color either. Everyone on the island knows the rules and is constantly aware of everyone else's eye color, and keeps a constant count of the total number of each (excluding themselves). However, they cannot otherwise communicate. So any given blue-eyed person can see 100 people with brown eyes and 99 people with blue eyes, but that does not tell them their own eye color; it could be 101 brown and 99 blue. Or 100 brown, 99 blue, and the one could have red eyes.
The Guru speaks only once (let's say at noon), on one day in all their endless years on the island. Standing before the islanders, she says the following:
"I can see someone with blue eyes."
Who leaves the island, and on what night?
There are no mirrors or reflecting surfaces, nothing dumb, It is not a trick question, and the answer is logical. It doesn't depend on tricky wording, and it doesn't involve people doing something silly like creating a sign language or doing genetics. The Guru is not making eye contact with anyone in particular; she's simply saying "I count at least one blue-eyed person on this island who isn't me."
And lastly, the answer is not "no one leaves."
Re:Riddle (Score:4, Funny)
You haul your ass to a bakery, shell out twenty bucks, and get a box or two full of cupcakes, then you go Cid Highwind on everyone.
"Siddown and eat your goddanm cupcakes!"
Re:Infinity (Score:4, Interesting)
Solution (Score:4, Interesting)
Re:Solution (Score:5, Interesting)
Disprufe(TM) by contradiction:
1. Suppose sqrt(2) ^ sqrt(2) ^ sqrt(2) ^
2. Then, sqrt(2) ^ (sqrt(2) ^ sqrt(2) ^
3. Hence, sqrt(2) ^ n = n.
4. Therefore, n obviously equals 4, because sqrt(2) ^ 4 = 4.
5. Hence, sqrt(2) ^ sqrt(2) ^ sqrt(2) ^
What's wrong with this logic?
Look and Say (Score:5, Informative)
Re:Phone Numbers (Score:5, Funny)
Re:Answer to the Sample Question (Score:5, Insightful)
Simply place any 18 coins into the second group and flip those over.
If you flip a coin over that was heads, it is now tails and is eliminated from consideration. If you flip a coin over that was tails, it marks with heads a coin selected that was not heads. Therefore after 18 coins are flipped, the number of heads in the second pile is equal to the number of heads that are left in the first pile.
Except... (Score:5, Informative)