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Brain Teaser

askbob
Posts: 7,254
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1/31/2011 10:26:03 PM
Posted: 5 years ago
There are 9 balls. One is slightly heavier than the other but you can't tell by feel.

There is a scale (old fashioned) in front of you. Multiple balls (no limit) can be put on each side.

What is the least number of uses of the scale to determine for a fact which ball is the heaviest.

If you know it, don't answer.

If you looked it up, don't answer

Explain your logic.
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mattrodstrom
Posts: 12,028
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1/31/2011 10:35:32 PM
Posted: 5 years ago
put 4 on either side... if they balance.. then it's the odd one out.

if they don't you take off two (one for either side)

then, if they're still not balanced you do it again...

when they do become balanced you know the odd one out is among the last two taken off..

so you weigh them against another one.

(not sure if there's a quicker way :/ )
"He who does not know how to put his will into things at least puts a meaning into them: that is, he believes there is a will in them already."

Metaphysics:
"The science.. which deals with the fundamental errors of mankind - but as if they were the fundamental truths."
askbob
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1/31/2011 10:36:48 PM
Posted: 5 years ago
At 1/31/2011 10:35:32 PM, mattrodstrom wrote:
put 4 on either side... if they balance.. then it's the odd one out.

if they don't you take off two (one for either side)

then, if they're still not balanced you do it again...

when they do become balanced you know the odd one out is among the last two taken off..

so you weigh them against another one.

(not sure if there's a quicker way :/ )

wrong
Me -Phil left the site in my charge. I have a recorded phone conversation to prove it.
kohai -If you're the owner, then do something useful like ip block him and get us away from juggle and on a dofferent host!
Me -haha you apparently don't know my history
Kohai - Maybe not, but that doesn't matter! You shoukd still listen to your community and quit being a tyrrant!
Me - i was being completely sarcastic
Kohai - then u misrepresented yourself by impersonating the owner—a violation of the tos
Awed
Posts: 44
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1/31/2011 10:48:11 PM
Posted: 5 years ago
Take 8/9 of the balls and divide it by two until you get the heaviest.

Put four balls on each side. If it's unbalanced, take the side that's heavier and put two on each side. From there, take the heavier side and put the two remaining balls on each side.

Ends up with three steps.
mattrodstrom
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1/31/2011 10:52:38 PM
Posted: 5 years ago
At 1/31/2011 10:48:11 PM, Awed wrote:
Take 8/9 of the balls and divide it by two until you get the heaviest.

Put four balls on each side. If it's unbalanced, take the side that's heavier and put two on each side. From there, take the heavier side and put the two remaining balls on each side.

Ends up with three steps.

Aha!.. I didn't think about knowing how it's "heavier" i was just thinkin to pick the one that's not the same weight...

that does improve things ;)
"He who does not know how to put his will into things at least puts a meaning into them: that is, he believes there is a will in them already."

Metaphysics:
"The science.. which deals with the fundamental errors of mankind - but as if they were the fundamental truths."
FREEDO
Posts: 21,057
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1/31/2011 10:53:23 PM
Posted: 5 years ago
Once.

Weighing too balls against each at a time, there is a chance that you may discovery it on the first try. Thus one is the least number of times you could need.
GRAND POOBAH OF DDO

fnord
mattrodstrom
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1/31/2011 10:54:24 PM
Posted: 5 years ago
At 1/31/2011 10:53:23 PM, FREEDO wrote:
Once.

Weighing too balls against each at a time, there is a chance that you may discovery it on the first try. Thus one is the least number of times you could need.

you could find it out by putting 8 on too...

so... I very much doubt it.
"He who does not know how to put his will into things at least puts a meaning into them: that is, he believes there is a will in them already."

Metaphysics:
"The science.. which deals with the fundamental errors of mankind - but as if they were the fundamental truths."
askbob
Posts: 7,254
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1/31/2011 10:57:14 PM
Posted: 5 years ago
all are wrong.
Me -Phil left the site in my charge. I have a recorded phone conversation to prove it.
kohai -If you're the owner, then do something useful like ip block him and get us away from juggle and on a dofferent host!
Me -haha you apparently don't know my history
Kohai - Maybe not, but that doesn't matter! You shoukd still listen to your community and quit being a tyrrant!
Me - i was being completely sarcastic
Kohai - then u misrepresented yourself by impersonating the owner—a violation of the tos
gavin.ogden
Posts: 1,729
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1/31/2011 10:58:53 PM
Posted: 5 years ago
At 1/31/2011 10:35:32 PM, mattrodstrom wrote:
put 4 on either side... if they balance.. then it's the odd one out.

if they don't you take off two (one for either side)

then, if they're still not balanced you do it again...

when they do become balanced you know the odd one out is among the last two taken off..

so you weigh them against another one.

(not sure if there's a quicker way :/ )

Dummy...
askbob
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1/31/2011 11:00:41 PM
Posted: 5 years ago
At 1/31/2011 10:53:23 PM, FREEDO wrote:
Once.

Weighing too balls against each at a time, there is a chance that you may discovery it on the first try. Thus one is the least number of times you could need.

for certain
Me -Phil left the site in my charge. I have a recorded phone conversation to prove it.
kohai -If you're the owner, then do something useful like ip block him and get us away from juggle and on a dofferent host!
Me -haha you apparently don't know my history
Kohai - Maybe not, but that doesn't matter! You shoukd still listen to your community and quit being a tyrrant!
Me - i was being completely sarcastic
Kohai - then u misrepresented yourself by impersonating the owner—a violation of the tos
askbob
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1/31/2011 11:08:54 PM
Posted: 5 years ago
At 1/31/2011 11:07:12 PM, mongeese wrote:
Wait, by "if you know it," what can that mean? I know the answer, but only because I solved it myself. Does that count?

if you legitimately figured it out without prior knowledge or help then sure give your answer
Me -Phil left the site in my charge. I have a recorded phone conversation to prove it.
kohai -If you're the owner, then do something useful like ip block him and get us away from juggle and on a dofferent host!
Me -haha you apparently don't know my history
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Kohai - then u misrepresented yourself by impersonating the owner—a violation of the tos
mongeese
Posts: 5,387
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1/31/2011 11:11:41 PM
Posted: 5 years ago
Prior knowledge? I definitely had significant prior knowledge of this, although it was a rather different problem, as it was unknown whether the mystery ball was heavier or lighter than the others. I won't post, I guess.
Awed
Posts: 44
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1/31/2011 11:19:25 PM
Posted: 5 years ago
ohhh. I get it now. This took me like 45 minutes. I'm sad.

Split the groups into 3. Weigh two of the three groups.

If the balance is tipped, then take the heavier side and weigh 2/3 of the balls. If the balance is equal, the ball that was omitted was the heavier one.

If the two groups in the beginning were equal, take the last group and do the above.

Ends up with two steps
askbob
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1/31/2011 11:20:11 PM
Posted: 5 years ago
At 1/31/2011 11:19:25 PM, Awed wrote:
ohhh. I get it now. This took me like 45 minutes. I'm sad.

Split the groups into 3. Weigh two of the three groups.

If the balance is tipped, then take the heavier side and weigh 2/3 of the balls. If the balance is equal, the ball that was omitted was the heavier one.

If the two groups in the beginning were equal, take the last group and do the above.

Ends up with two steps

This is correct
Me -Phil left the site in my charge. I have a recorded phone conversation to prove it.
kohai -If you're the owner, then do something useful like ip block him and get us away from juggle and on a dofferent host!
Me -haha you apparently don't know my history
Kohai - Maybe not, but that doesn't matter! You shoukd still listen to your community and quit being a tyrrant!
Me - i was being completely sarcastic
Kohai - then u misrepresented yourself by impersonating the owner—a violation of the tos
askbob
Posts: 7,254
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1/31/2011 11:21:19 PM
Posted: 5 years ago
Second Brain Teaser.

It is 9:30 and 22 seconds on an analog clock.

What is the angle between the hour hand and the second hand.

Show all math.
Me -Phil left the site in my charge. I have a recorded phone conversation to prove it.
kohai -If you're the owner, then do something useful like ip block him and get us away from juggle and on a dofferent host!
Me -haha you apparently don't know my history
Kohai - Maybe not, but that doesn't matter! You shoukd still listen to your community and quit being a tyrrant!
Me - i was being completely sarcastic
Kohai - then u misrepresented yourself by impersonating the owner—a violation of the tos
mongeese
Posts: 5,387
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1/31/2011 11:29:56 PM
Posted: 5 years ago
The hour hand makes circles of 12 hours = 720 minutes = 43200 seconds.
The hour hand is currently at 9:30:22, or 34222 seconds.
Threfore, it is 79.22% of the way done, with an angle measure of 285.183.

The second hand makes circles of 60 seconds.
The second hand is currently at 22 seconds.
Therefore, it is 36.667% of the way done, with an angle measure of 132.

The difference would be 285.183 - 132 = 153.183 degrees, or 153 degrees and 11 minutes.
Awed
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1/31/2011 11:33:49 PM
Posted: 5 years ago
9 hours = 270 degrees
(30min/720min)*360 degrees = 15 degrees
(22sec/43200sec)*360 degrees = 11/60 degrees
Add all of them up, and you get 285.18333 degrees

(22sec/60sec)*360 degrees = 132 degrees.

285.18333 - 132 = 153.15333 or 153 and 11/60 degrees.
badger
Posts: 11,793
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2/1/2011 6:47:32 AM
Posted: 5 years ago
easy!

here's a similar one: you've 6 balls.. one is either lighter or heavier but you don't know which it is, or whether it's lighter or heavier.. how many times to determine which is the odd ball and whether it's lighter or heavier?
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askbob
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2/1/2011 7:23:39 AM
Posted: 5 years ago
At 1/31/2011 11:29:56 PM, mongeese wrote:
The hour hand makes circles of 12 hours = 720 minutes = 43200 seconds.
The hour hand is currently at 9:30:22, or 34222 seconds.
Threfore, it is 79.22% of the way done, with an angle measure of 285.183.

The second hand makes circles of 60 seconds.
The second hand is currently at 22 seconds.
Therefore, it is 36.667% of the way done, with an angle measure of 132.

The difference would be 285.183 - 132 = 153.183 degrees, or 153 degrees and 11 minutes.

excellent use of logic
Me -Phil left the site in my charge. I have a recorded phone conversation to prove it.
kohai -If you're the owner, then do something useful like ip block him and get us away from juggle and on a dofferent host!
Me -haha you apparently don't know my history
Kohai - Maybe not, but that doesn't matter! You shoukd still listen to your community and quit being a tyrrant!
Me - i was being completely sarcastic
Kohai - then u misrepresented yourself by impersonating the owner—a violation of the tos
askbob
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2/1/2011 1:45:33 PM
Posted: 5 years ago
At 2/1/2011 6:47:32 AM, badger wrote:
easy!

here's a similar one: you've 6 balls.. one is either lighter or heavier but you don't know which it is, or whether it's lighter or heavier.. how many times to determine which is the odd ball and whether it's lighter or heavier?

Not really following this
Me -Phil left the site in my charge. I have a recorded phone conversation to prove it.
kohai -If you're the owner, then do something useful like ip block him and get us away from juggle and on a dofferent host!
Me -haha you apparently don't know my history
Kohai - Maybe not, but that doesn't matter! You shoukd still listen to your community and quit being a tyrrant!
Me - i was being completely sarcastic
Kohai - then u misrepresented yourself by impersonating the owner—a violation of the tos
badger
Posts: 11,793
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2/1/2011 1:59:59 PM
Posted: 5 years ago
At 2/1/2011 1:45:33 PM, askbob wrote:
At 2/1/2011 6:47:32 AM, badger wrote:
easy!

here's a similar one: you've 6 balls.. one is either lighter or heavier but you don't know which it is, or whether it's lighter or heavier.. how many times to determine which is the odd ball and whether it's lighter or heavier?

Not really following this

what about it aren't you following..

6 balls

one is either lighter or heavier..

you don't know which ball it is

and you don't know if it's lighter or heavier

you've to find out the two above..

how many uses of the scale?
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askbob
Posts: 7,254
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2/1/2011 2:04:17 PM
Posted: 5 years ago
At 2/1/2011 1:59:59 PM, badger wrote:
At 2/1/2011 1:45:33 PM, askbob wrote:
At 2/1/2011 6:47:32 AM, badger wrote:
easy!

here's a similar one: you've 6 balls.. one is either lighter or heavier but you don't know which it is, or whether it's lighter or heavier.. how many times to determine which is the odd ball and whether it's lighter or heavier?

Not really following this

what about it aren't you following..

6 balls

one is either lighter or heavier..

you don't know which ball it is

and you don't know if it's lighter or heavier

you've to find out the two above..

how many uses of the scale?

ahh didn't know that it also used a scale.

2 times same concept as the last one.

2 on one side of scale

2 on other side of scale

2 sitting on table unweighed

If they balanced then split the ones on the table

If one side is heavier then split the heavier side.

Heaviest ball on second weight is the ball you want.
Me -Phil left the site in my charge. I have a recorded phone conversation to prove it.
kohai -If you're the owner, then do something useful like ip block him and get us away from juggle and on a dofferent host!
Me -haha you apparently don't know my history
Kohai - Maybe not, but that doesn't matter! You shoukd still listen to your community and quit being a tyrrant!
Me - i was being completely sarcastic
Kohai - then u misrepresented yourself by impersonating the owner—a violation of the tos
badger
Posts: 11,793
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2/1/2011 2:06:06 PM
Posted: 5 years ago
At 2/1/2011 2:04:17 PM, askbob wrote:
At 2/1/2011 1:59:59 PM, badger wrote:
At 2/1/2011 1:45:33 PM, askbob wrote:
At 2/1/2011 6:47:32 AM, badger wrote:
easy!

here's a similar one: you've 6 balls.. one is either lighter or heavier but you don't know which it is, or whether it's lighter or heavier.. how many times to determine which is the odd ball and whether it's lighter or heavier?

Not really following this

what about it aren't you following..

6 balls

one is either lighter or heavier..

you don't know which ball it is

and you don't know if it's lighter or heavier

you've to find out the two above..

how many uses of the scale?

ahh didn't know that it also used a scale.

2 times same concept as the last one.

2 on one side of scale

2 on other side of scale

2 sitting on table unweighed

If they balanced then split the ones on the table

If one side is heavier then split the heavier side.

Heaviest ball on second weight is the ball you want.

ammm.. no.. read it again..
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FREEDO
Posts: 21,057
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2/1/2011 2:06:42 PM
Posted: 5 years ago
At 2/1/2011 1:59:59 PM, badger wrote:
At 2/1/2011 1:45:33 PM, askbob wrote:
At 2/1/2011 6:47:32 AM, badger wrote:
easy!

here's a similar one: you've 6 balls.. one is either lighter or heavier but you don't know which it is, or whether it's lighter or heavier.. how many times to determine which is the odd ball and whether it's lighter or heavier?

Not really following this

what about it aren't you following..

6 balls

one is either lighter or heavier..

you don't know which ball it is

and you don't know if it's lighter or heavier

you've to find out the two above..

how many uses of the scale?

Happy 5,000th post.
GRAND POOBAH OF DDO

fnord
badger
Posts: 11,793
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2/1/2011 2:07:40 PM
Posted: 5 years ago
At 2/1/2011 2:06:42 PM, FREEDO wrote:
At 2/1/2011 1:59:59 PM, badger wrote:
At 2/1/2011 1:45:33 PM, askbob wrote:
At 2/1/2011 6:47:32 AM, badger wrote:
easy!

here's a similar one: you've 6 balls.. one is either lighter or heavier but you don't know which it is, or whether it's lighter or heavier.. how many times to determine which is the odd ball and whether it's lighter or heavier?

Not really following this

what about it aren't you following..

6 balls

one is either lighter or heavier..

you don't know which ball it is

and you don't know if it's lighter or heavier

you've to find out the two above..

how many uses of the scale?

Happy 5,000th post.

woo!
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