Brain Teasers and Maths Puzzles

[Zyx]

I broke down and Google'd the answer. Oh my dear god, this was a good puzzle. I'm now very sorry I did not try harder to solve this. As a hint, it's all about the two piles and the number of cards in each pile.

[Pater Alf]

Another question: Will somebody tell him if he has the right solution? In that case he could try every possible combination of piles and turned cards. Would probably take forever, but sooner or later he would come across the solution.

[eMTe]

If somebody would tell him if he's right or not it would undermine the very sense of this puzzle - that he knows the solution. Sure you can solve this puzzle by accident, as many other puzzles, but it's not the goal, huh?

[Pater Alf]

Well, it wouldn't be by accident. You could come up with a mathematical/logical system how to flip cards and change pile's height that would sooner or later bring the solution. But the blind man wouldn't know by himself. If you say that nobody talks to him, I won't waste my time and think in that direction any longer.

[eMTe]

Heh, you don't have Wallander/Beck spirit. They never give up.

[Pater Alf]

You misunderstood. I don't give up. I just leave a theory alone from which you told me it is wrong. Will come up with a new one though.

[Tormuse]

(I'm still puzzling about this too; I'll come back to it after I've given it some more thought)

[Pater Alf]

I just found out that the solution to this puzzle is completely simple:

The blind man takes the whole deck of cards and flips the first ten cards around (making a second pile that way). At that point there will always be the same ammount of head-up-cards in both piles. If there were no head-up-cards among the first ten in the original pile there will be 10:10 after that, if there was one card, it will be 9:9 after that, if there were two, it will be 8:8 and so on...

Don't know why I didn't see that when I first picked up the deck of cards some days ago.

[Tormuse]

Is it really that simple? Crap! I think I was making it too complicated for myself! I figured that you had to arrange them in such a way that it doesn't matter whether the cards you're turning are face-up or face-down to start with, but now I feel dumb that the answer was so simple. Oh well... Maybe I'll get the next one.

Congrats, Pater Alf!

[eMTe]

And we have a winner. It was easy, wasn't it?

Next one, please?

[Pater Alf]

I don't have a new puzzle at the moment, so please feel free to post another one.

[eMTe]

This one is easier.

You have two indistinguishable dynamite fuses, both of the same length (1 meter). Also, you know that it takes 1 hour for each to burn completely. Now, how to measure three quarters of an hour with them?

Before you start asking lateral questions - you are sitting naked on a desolate desert on a desolate planet in the desolate star system and you don't have neither scissors nor ruler. However, for reasons beyond your understanding, you were able to come into possession of matchbox.

[Zyx]

Do the fuses burn at a constant rate?

[Zyx]

First, start burning the first one from both ends and the second one from one end. When the first one is completely burned (after half an hour), also start to burn the second one from both ends. The other fuse had half an hour to go, and when burned from both ends, just 15 minutes so the total show lasts for 45 minutes.

[Tormuse]

At first, I misread it and thought there was dynamite attached to the fuses and I thought Zyx blew himself up!

[eMTe]

No, he's been teleported back to Earth and allowed to post next puzzle.

[Zyx]

This is a classic, so I'm sorry if it has been already mentioned in this thread. I hate this puzzle.

This weekend, I'm going to go out on the streets of Helsinki and start to ask random people if they have (exactly) two children, and whether one of them is a girl born on a Sunday. (This is linked to one Mayan prophecy about Armageddon, so it's quite important to find this child.) It will take me some time, but eventually I will find a person that answers yes.

Finland is a statistically strange country that due to this Mayan prophecy, everyone I ask has had an equal chance of giving birth to either boy or a girl and our maternity wards are so efficient that births are equally distributed among the week. Also, the births are statistically independent so no twins or anything. It's a curse, really.

It doesn't really affect the prophecy, but what is the probability that the person answering yes has two girls?

[eMTe]

1/35? 1/42?

[Zyx]

Nope, note that the other girl doesn't have to be born on a Sunday. They Mayans were funny that way.

[eMTe]

1/63?