Knights Reborn

~Double Post Fixed~

Btw 100th post on this topic!

MasterM wrote:jawfy, feel free to post yours

Honestly? Well, my opinion is if no-one else took a stab at Fazz's they certainly won't bother with mine. My puzzles seem to either cater for children or math buffs. If I think of kind of middle ground one I'll post:P

Or in the meantime, another child's play one... As this was the one I sent to MasterM and he said it was too simple, so, here goes...

It's dark at night time and you need a pair of socks. In the sock drawer are 15 dark blue socks and 15 dark green socks, but they all look black to you. You need a pair and you don't care what color. What in the minimum number of socks you need to take out to ensure you have a pair?

*cough* three

also, since i am a child and a math buff, your puzzles would probably suit me

ok so i'm back now (woot) so i'll maybe kind of sorta attempt to post now.

here's a good one:

Three different numbers are chosen at random, and one is written on each of three slips of paper. The slips are then placed face down on the table. The objective is to choose the slip upon which is written the largest number.

Here are the rules: You can turn over any slip of paper and look at the amount written on it. If for any reason you think this is the largest, you're done; you keep it. Otherwise you discard it and turn over a second slip. Again, if you think this is the one with the biggest number, you keep that one and the game is over. If you don't, you discard that one too.
And you're stuck with the third.
The chance of getting the highest number is one in three. Or is it? Is there a strategy by which you can improve the odds?

Complex game theory, anyone who has studied AI *cough* or seen the movie Good Will Hunting should know how to solve this.

But, sorry MasterM, I'd given up on this thread... That no-one could solve a riddle for 10 to 15 year olds indicates that this is aimed at the wrong target audience.

Jawfin wrote:But, sorry MasterM, I'd given up on this thread... That no-one could solve a riddle for 10 to 15 year olds indicates that this is aimed at the wrong target audience.

, i found the actual 'riddle amusing'. i read it and 3 was sooo obvious. then i almost convinced myself that it wasnt 3, coz that was just too easy, and there must be some obvious angle that im missing. But apparentally not, the answer was 3...

and i know the latest puzzle, so i wont be posting for it :p

for anyone who cares...

Well, it turns out there is a way to improve the odds. Let's name our fake contestant Vinnie. Vinnie's strategy changes the odds to one in two. Here's how he does it: First, he picks one of the three slips of paper at random and looks at the number. No matter what the number is, he throws the slip of paper away. But he remembers that number. If the second slip he chooses has a higher number than the first, he sticks with that one. If the number on the second slip is lower than the first number, he goes on to the third slip.

Here's an example. Let's say for the sake of simplicity that the three slips are numbered 1000, 500, and 10.



Let's say Vinnie picks the slip with the 1000. We know he can't possibly win because, according to his rules, he's going to throw that slip out. No matter what he does he loses, whether he picks 500 next or 10. So, Vinnie loses—twice.



Now, let's look at what happens if Vinnie starts with the slip with the 500 on it. If he picks the 10 next, according to his rules, he throws that slip away and goes to the 1000.

He wins!

And if Vinnie picks the 1000 next, he wins again!



Finally, if he picks up the slip with the 10 on it first, he'll do, what?

Throw it out. Those are his rules.



And if he should be unfortunate enough to pick up the one that says 500 next, he's going to keep it and he's going to lose. However, if his second choice is not the 500 one but the 1000 one, he's gonna keep that slip—and he'll win.



If you look at all six scenarios Vinnie will win three times out of six.

This one is pretty good, though it is a bit long, so bear with me

Imagine there is a hat sitting on the table. And there are two contestants. Tommy, will be one of the contestants, and we'll call the other one Vinnie.


Tommy reaches into the hat and pulls out a number. Then, Vinnie does the same. Now, the reason this hat is magical is that, no matter what number Tommy pulls out, Vinnie will always pull out a number that is either one above or one below Tommy's number. For example, if Tommy pulls out a two, Tommy knows Vinnie has pulled out either a one or a three.

So, each person pulls out a number. Let's say Tommy picks three and Vinnie picks two. I'm the moderator, and I ask Tommy, "Do you know what number Vinnie has?" Tommy looks at his number, which is 3, and says, "No, I don't."


I then ask Vinnie, "Do you know what number Tommy has?" He looks at his number two and says, "Yes." He knows Tommy has to have a 3.



Now, here's the tricky part:

Regardless of the numbers that are picked, and assuming that both contestants answer truthfully, if I keep asking the question of both of them, eventually one contestant will know what number the other contestant has.

In other words, if I ask Tommy, then ask Vinnie, then Tommy again... then Vinnie again... eventually one of them will know the other's number.

The question is this:

How come is that?

*Spoiler*
The answer is pretty much given in the question with this statement: -

• I then ask Vinnie, "Do you know what number Tommy has?" He looks at his number two and says, "Yes." He knows Tommy has to have a 3.

As they will eventually work their way down to zero and/or up to infinity. I am assuming they'll hit zero first! I also assume you don't consider zero or negatives as numbers...!