New "brain strecher" ...

teutonu

teutonu

1
Hi all,

due to a large number of requests :rolleyes: (in fact only Midnightangel asked for a new brain strecher, but it was enough for me to quickly post until he also makes up his mind :p ) here is a new problem for your little neurons:

You have 9 balls (not that kind of balls !!!! you would like to have :D guys).
The balls are looking all the same. But one ball has a slightly different weight than the other 8. You cannot say by hand which one it is - so little is the difference - so you have to weigh them in a balance.

The question: how many times do you HAVE to weigh the balls to find out (with 100%) which ball has another weight ?

Note 1: there are a lot of solutions, but we are looking for the most efficient solution. So as few as possible weighing processes !!!

Note 2: for those who already know this problem, please don't enter the game. Keep the answer for you and let the others solve it.

OK, 1,2,3 START ! If you think you have the best answer send it to me via PM. Please do not post questions or clues, so as to have same conditions for all. Waiting ... :cool:
 
teutonu

teutonu

1
Hello everybody !!!

Since it has been enough time to solve this problem and since very few even bothered to think about it, I assume that it is about time to solve it.

There has been one person to give the correct answer: whytless physh - cheers to you :) .

And here is the answer and I quote from what whytless physh has written:

If you take the nine balls and put them groups of three, weigh two of those sets (doesn't matter which two), that will get you down to three balls with one try. Take two balls from the heavy side (or the unweighed ones if the original sets balance) and weigh those. That will leave the heavy one pretty obvious in only two tries.
Click to expand...
I assume that this kind of "mind sports" does not amuse you much, so I will cut it. When there is so much useful info on this forum, why bother to have a little fun ?? ;)

Greetz
 
B

borogovio

1
Sorry to disagree, but this solution takes for granted that the one with a 'different weight' is heavier !!! What if it is lighter than the other 8? The provided solution wouldn't work.

BTW, teutonu - have you solved the problem about the Hare of March & Mad Hatter ?
 
davydz

davydz

1
I agree with borogovio, If the ball was lighter then youve lost the plot to start with. Best I could do was four weighings to be sure of which ball was lighter or heavier than the others.
 
teutonu

teutonu

1
Hey all,

@boro
the provided solution would work , BUT I SOULD HAVE TOLD YOU THAT THE DIFFERENT BALL IS LIGHTER.

so to conclude: YES I MESSED IT UP.
NO, THIS DOES NOT TAKE AWAY THE CONGRATULATIONS FOR THE ONE WHO SOLVED IT.

But again, you are all correct when you say that in order to be solvable i should have specified that it is heavier (or lighter - works same way)!!!

AAAAAAGGGHHH!!!! I screwed up ... ok, i'm going to the corner, staying there face to wall for the next half an hour and i will be ashame. :(
 
B

borogovio

1
I came across this problem, with the ball weighing different (unknown whether lighter or heavier), a long time ago, & it was a hell to solve it with THREE weighings.
Unfortunately, I lost the book with the solution
 
P

Psycho2000

1
I think there is a solution if the ball is lighter -- try this.....

Divide balls into 3 groups (2 groups of 4 and 1 by itself)

1. Get scales (old style - with 2 pans) and put four on each side. If scales are level - the one left out is the lighter ball. If one side is lighter than the other, then this group of 4 contains the lighter one. Discard the other side.

2. Split the group of 4 into 2 groups of two and repeat above.

By this method, you should be able to determine the lighter one in maximum of three weighings....

Cheers

P2000
 
P

Psycho2000

1
You can check it by using one of the other 8 discarded balls.

Ie - if you are left with 2 balls and the scales are not even, then take off one of the balls (from the "up" side for example) and replace it with another. If the scales level out the odd ball out was lighter and it is the one you took off. If the scales stay the same, the odd ball out is heavy and it is on the other end...

Cheers

P2000

(Too much thinking, I need a break now - better get back to work !). :)
 
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