This is a difficult puzzle that a colleague sent me.
Took me several days to work it out.
Please don’t cheat by googling it!
Good luck!
You have 12 balls identical in size and appearance but 1 is an odd weight (could be either light or heavy). You have a set scales (balance) which will give 3 possible readings:- Left = Right, Left > Right or Left < Right. You have only 3 chances to weigh the balls in any combination using the scales. Determine which ball is the odd one and if it’s heavier or lighter than the rest. How do you do it?
Simon Macks
Mortgage Broker
http://www.mortgagehunter.com.au
0425 228 985Comments may not be relevant to individual circumstances. If you intend making any investment, financial or taxation decision you should consult a professional adviser.
12 balls: No. 1 to 12.
Take A= No. 1-3, B= No.4-6, C= No. 7-9, D=No. 10-12.
If A = B Then
C <> D
If 7 = 8 then
Answer = 9
Else
Answer is 7 or 8
Else
If 1 = 2 then
Answer = 3
Else
Answer is 1 or 2Warm Regards
ChanDollars
[Keep going, you’re on your way to Frolic Freedom!]Chan,
Good try but we don’t know if the different ball is heavier or lighter.
So when you say C<>D you don’t know which group has the odd ball.
Keep thinking.
Simon Macks
Mortgage Broker
http://www.mortgagehunter.com.au
0425 228 985Comments may not be relevant to individual circumstances. If you intend making any investment, financial or taxation decision you should consult a professional adviser.
This is a good thinking game and I am trying very hard here!
Warm Regards
ChanDollars
[Keep going, you’re on your way to Frolic Freedom!]As you are putting the balls on the scale, you put one on the left side, one on the right side. Then you have an expected pattern. Left goes down, back to level, left goes down, back to level. If you get something different to this pattern, i.e. left goes down, stays down, you can narrow the ball down to two balls…compare these balls to one of the normal balls and you can find out if it is heavier or lighter.
Close? or do I have to put the balls on at the same time?
OK here is the answer, I hope:
1. Put 5 balls on left and 5 balls on right! Therefore, 2 balls not on scale. If Left = right then the 2 balls is the answer. ie. take one of the two and one of the ten ball and you be able to find out. (only two steps here)
2. If Left <> Right then that mean 2 balls left is the standard ball. Now take 5 balls from left, keep one and put 2 on left and 2 on right. if left = right then the 1 ball not on the scale is the answer. If left <> right then take one ball on the scale and compare to anyone on scale.Warm Regards
ChanDollars
[Keep going, you’re on your way to Frolic Freedom!]Originally posted by JapanScott:As you are putting the balls on the scale, you put one on the left side, one on the right side. Then you have an expected pattern. Left goes down, back to level, left goes down, back to level. If you get something different to this pattern, i.e. left goes down, stays down, you can narrow the ball down to two balls…compare these balls to one of the normal balls and you can find out if it is heavier or lighter.
Close? or do I have to put the balls on at the same time?
I think JapanScott is right?
Cheers,
sisJapanscott,
you only have the three weighings.
Chan,
You are on the right track. But remember you don’t know if the odd ball is heavier or lighter. So
If left <> right then take one ball on the scale and compare to anyone on scale.
Which ball? You have two weighing left and four balls?
if they match then which of the other two balls is it? The heavier one or lighter one?Keep trying – you are heading in the right direction but forget the 5 + 5 + 2 groups. Try a different combination!
C’mon guys there must be some more smart folks out there!
Simon Macks
Mortgage Broker
http://www.mortgagehunter.com.au
0425 228 985Comments may not be relevant to individual circumstances. If you intend making any investment, financial or taxation decision you should consult a professional adviser.
Mortgage Hunter,
Because of this quiz I lose a lot of posting today…lol…
Back to the quiz…thinking…
Any clues?
Warm Regards
ChanDollars
[Keep going, you’re on your way to Frolic Freedom!]12 Balls:
4A = 2AA+2AB
4B = 2BA+2BB
4C = 2CA+2CB4A VS 4B
if 4A = 4B then
2CA vs 2AA
if 2CA = 2AA
1CAAA vs 1AAA
if 1CAAA = 1AAA
1CAAB is the solution
if 4A <> 4B
4C is the standard ball
2AA vs 2CA
1AAA vs 1CAA
solutionWarm Regards
ChanDollars
[Keep going, you’re on your way to Frolic Freedom!]OK Chan my friend,
try this
3 groups of four
Cheers,
Simon Macks
Mortgage Broker
http://www.mortgagehunter.com.au
0425 228 985Comments may not be relevant to individual circumstances. If you intend making any investment, financial or taxation decision you should consult a professional adviser.
Am I on the right track?
Training finish, going home.
Warm Regards
ChanDollars
[Keep going, you’re on your way to Frolic Freedom!]Chan,
You may be right. You lost me a little with your naming methodology.
here is my answer:
Number the balls 1, 2, 3….., 10, 11, 12
Weigh 1, 2, 3, 4 vs 5, 6, 7, 8 with 3 possible outcomes:-1/ If they balance then 9,10,11,12 have the odd ball, so weigh 6,7,8 vs 9,10,11 with 3 possible outcomes:-
i/ If 6,7,8 vs 9,10,11 balances, 12 is the odd ball. Weigh it against any other ball to determine if heavy or light.
ii/ If 9,10,11 is heavy then they contain a heavy ball. Weigh 9 vs 10, if balanced then 11 is the odd heavy ball, else the heavier of 9 or 10 is the odd heavy ball.
iii/ If 9,10,11 is light then they contain a light ball. Weigh 9 vs 10, if balanced then 11 is the odd light ball, else the lighter of 9 or 10 is the odd light ball.2/ If 5,6,7,8 > 1,2,3,4 then either 5,6,7,8 contains a heavy ball or 1,2,3,4 contains a light ball so weigh 1,2,5 vs 3,6,12 with 3 possible outcomes:-
i/ If 1,2,5 vs 3,6,12 balances, then either 4 is the odd light ball or 7 or 8 is the odd heavy ball. Weigh 7 vs 8, if they balance then 4 is the odd light ball, or the heaviest of 7 vs 8 is the odd heavy ball.
ii/ If 3,6,12 is heavy then either 6 is the odd heavy ball or 1 or 2 is the odd light ball. Weigh 1 vs 2, if balanced then 6 is the odd heavy ball, or the lighest of 1 vs 2 is the odd light ball.
iii/ If 3,6,12 is light then either 3 is light or 5 is heavy. Weigh 3 against any other ball, if balanced then 5 is the odd heavy ball else 3 is the odd light ball.3/ If 1,2,3,4 > 5,6,7,8 then either 1,2,3,4 contains a heavy ball or 5,6,7,8 contains a light ball so weigh 5,6,1 vs 7,2,12 with 3 possible outcomes:-
i/ If 5,6,1 vs 7,2,12 balances, then either 8 is the odd light ball or 3 or 4 is the odd heavy ball. Weigh 3 vs 4, if they balance then 8 is the odd light ball, or the heaviest of 3 vs 4 is the odd heavy ball.
ii/ If 7,2,12 is heavy then either 2 is the odd heavy ball or 5 or 6 is the odd light ball. Weigh 5 vs 6, if balanced then 2 is the odd heavy ball, or the lighest of 5 vs 6 is the odd light ball.iii/ If 7,2,12 is light then either 7 is light or 1 is heavy. Weigh 7 against any other ball, if balanced then 1 is the odd heavy ball else 7 is the odd light ball.
Simon Macks
Mortgage Broker
http://www.mortgagehunter.com.au
0425 228 985Comments may not be relevant to individual circumstances. If you intend making any investment, financial or taxation decision you should consult a professional adviser.
Originally posted by MortgageHunter:Chan,
You may be right. You lost me a little with your naming methodology.
here is my answer:
Number the balls 1, 2, 3….., 10, 11, 12
Weigh 1, 2, 3, 4 vs 5, 6, 7, 8 with 3 possible outcomes:-1/ If they balance then 9,10,11,12 have the odd ball, so weigh 6,7,8 vs 9,10,11 with 3 possible outcomes:-
i/ If 6,7,8 vs 9,10,11 balances, 12 is the odd ball. Weigh it against any other ball to determine if heavy or light.
ii/ If 9,10,11 is heavy then they contain a heavy ball. Weigh 9 vs 10, if balanced then 11 is the odd heavy ball, else the heavier of 9 or 10 is the odd heavy ball.
iii/ If 9,10,11 is light then they contain a light ball. Weigh 9 vs 10, if balanced then 11 is the odd light ball, else the lighter of 9 or 10 is the odd light ball.2/ If 5,6,7,8 > 1,2,3,4 then either 5,6,7,8 contains a heavy ball or 1,2,3,4 contains a light ball so weigh 1,2,5 vs 3,6,12 with 3 possible outcomes:-
i/ If 1,2,5 vs 3,6,12 balances, then either 4 is the odd light ball or 7 or 8 is the odd heavy ball. Weigh 7 vs 8, if they balance then 4 is the odd light ball, or the heaviest of 7 vs 8 is the odd heavy ball.
ii/ If 3,6,12 is heavy then either 6 is the odd heavy ball or 1 or 2 is the odd light ball. Weigh 1 vs 2, if balanced then 6 is the odd heavy ball, or the lighest of 1 vs 2 is the odd light ball.
iii/ If 3,6,12 is light then either 3 is light or 5 is heavy. Weigh 3 against any other ball, if balanced then 5 is the odd heavy ball else 3 is the odd light ball.3/ If 1,2,3,4 > 5,6,7,8 then either 1,2,3,4 contains a heavy ball or 5,6,7,8 contains a light ball so weigh 5,6,1 vs 7,2,12 with 3 possible outcomes:-
i/ If 5,6,1 vs 7,2,12 balances, then either 8 is the odd light ball or 3 or 4 is the odd heavy ball. Weigh 3 vs 4, if they balance then 8 is the odd light ball, or the heaviest of 3 vs 4 is the odd heavy ball.
ii/ If 7,2,12 is heavy then either 2 is the odd heavy ball or 5 or 6 is the odd light ball. Weigh 5 vs 6, if balanced then 2 is the odd heavy ball, or the lighest of 5 vs 6 is the odd light ball.iii/ If 7,2,12 is light then either 7 is light or 1 is heavy. Weigh 7 against any other ball, if balanced then 1 is the odd heavy ball else 7 is the odd light ball.
Simon Macks
Mortgage Broker
http://www.mortgagehunter.com.au
0425 228 985Comments may not be relevant to individual circumstances. If you intend making any investment, financial or taxation decision you should consult a professional adviser.
Mortgage Hunter,
That’s the way I am trying to do! So I was half right. Bloody spent the whole afternoon solving this problem.
Warm Regards
ChanDollars
[Keep going, you’re on your way to Frolic Freedom!]I haven’t even tried to solve the puzzle – just read the postings so far – and my head hurts.
Go Chan$…
Originally posted by BlackJack:I haven’t even tried to solve the puzzle – just read the postings so far – and my head hurts.
Go Chan$…
what about me, can’t stop thinking about it even on the train on the way back home…lol…
Warm Regards
ChanDollars
[Keep going, you’re on your way to Frolic Freedom!]The explanation sounds hard.
When I worked it out we got 12 bits of paper numbered 1-12.
My wife chose a number that was heavier or lighter and then told me each time which way the scales would go.
Works every time!
It is easy in practice – hard to communicate!
Well done team. These things are a bit of a hobby of mine [
]Cheers,
Simon Macks
Mortgage Broker
http://www.mortgagehunter.com.au
0425 228 985Comments may not be relevant to individual circumstances. If you intend making any investment, financial or taxation decision you should consult a professional adviser.
Originally posted by MortgageHunter:The explanation sounds hard.
When I worked it out we got 12 bits of paper numbered 1-12.
My wife chose a number that was heavier or lighter and then told me each time which way the scales would go.
Works every time!
It is easy in practice – hard to communicate!
Well done team. These things are a bit of a hobby of mine [
]Cheers,
Simon Macks
Mortgage Broker
http://www.mortgagehunter.com.au
0425 228 985Comments may not be relevant to individual circumstances. If you intend making any investment, financial or taxation decision you should consult a professional adviser.
I think it is a great hobby, may be I should go back to where I was before which was my kind of thing as well.
Thank you for sharing Mortgage Hunter.
Warm Regards
ChanDollars
[Keep going, you’re on your way to Frolic Freedom!]Simon said:
here is my answer:
Number the balls 1, 2, 3….., 10, 11, 12
Weigh 1, 2, 3, 4 vs 5, 6, 7, 8 with 3 possible outcomes:-1/ If they balance then 9,10,11,12 have the odd ball, so weigh 6,7,8 vs 9,10,11 with 3 possible outcomes:-
i/ If 6,7,8 vs 9,10,11 balances, 12 is the odd ball. Weigh it against any other ball to determine if heavy or light.
ii/ If 9,10,11 is heavy then they contain a heavy ball. Weigh 9 vs 10, if balanced then 11 is the odd heavy ball, else the heavier of 9 or 10 is the odd heavy ball.
iii/ If 9,10,11 is light then they contain a light ball. Weigh 9 vs 10, if balanced then 11 is the odd light ball, else the lighter of 9 or 10 is the odd light ball.2/ If 5,6,7,8 > 1,2,3,4 then either 5,6,7,8 contains a heavy ball or 1,2,3,4 contains a light ball so weigh 1,2,5 vs 3,6,12 with 3 possible outcomes:-
i/ If 1,2,5 vs 3,6,12 balances, then either 4 is the odd light ball or 7 or 8 is the odd heavy ball. Weigh 7 vs 8, if they balance then 4 is the odd light ball, or the heaviest of 7 vs 8 is the odd heavy ball.
ii/ If 3,6,12 is heavy then either 6 is the odd heavy ball or 1 or 2 is the odd light ball. Weigh 1 vs 2, if balanced then 6 is the odd heavy ball, or the lighest of 1 vs 2 is the odd light ball.
iii/ If 3,6,12 is light then either 3 is light or 5 is heavy. Weigh 3 against any other ball, if balanced then 5 is the odd heavy ball else 3 is the odd light ball.3/ If 1,2,3,4 > 5,6,7,8 then either 1,2,3,4 contains a heavy ball or 5,6,7,8 contains a light ball so weigh 5,6,1 vs 7,2,12 with 3 possible outcomes:-
i/ If 5,6,1 vs 7,2,12 balances, then either 8 is the odd light ball or 3 or 4 is the odd heavy ball. Weigh 3 vs 4, if they balance then 8 is the odd light ball, or the heaviest of 3 vs 4 is the odd heavy ball.
ii/ If 7,2,12 is heavy then either 2 is the odd heavy ball or 5 or 6 is the odd light ball. Weigh 5 vs 6, if balanced then 2 is the odd heavy ball, or the lighest of 5 vs 6 is the odd light ball.iii/ If 7,2,12 is light then either 7 is light or 1 is heavy. Weigh 7 against any other ball, if balanced then 1 is the odd heavy ball else 7 is the odd light ball.
Oh dear Simon.. that makes my head feel like I was born without a brain. Lucky property investing is not a riddle!
kay henry
I think property investing is much harder than this riddle. It look simple but it is not.
Warm Regards
ChanDollars
[Keep going, you’re on your way to Frolic Freedom!]
]
You must be logged in to reply to this topic. If you don't have an account, you can register here.
