Register Guidelines E-Books Search Today's Posts Mark Forums Read

Go Back   MobileRead Forums > Miscellaneous > Lounge

Notices

Reply
 
Thread Tools Search this Thread
Old 06-14-2010, 06:39 AM   #1
pdurrant
The Grand Mouse
pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.
 
pdurrant's Avatar
 
Posts: 31,712
Karma: 87828960
Join Date: Jul 2007
Location: Norfolk, England
Device: NOOK ST GlowLight
Twelve coins problem

A variant on a classic problem.



I have twelve apparently identical coins. I keep them safe in a small bag, tucked away under my jacket. Well, in fact in two bags — so that even if one bag gets stolen, I won't have lost all my money (eggs and baskets, you know). The bags are not very pretty — just mass-produced things — but they are strong enough to hold the coins securely.

I suspect that one of my coins is a fake, and is either slightly heavier or slightly lighter than the others, and I need nine good coins to buy something I need to get today. Passing fake money is severely punished, so I can't just take a chance by picking nine of my twelve at random.

Unfortunately, the only scales available to me are owned by a miser who charges one coin per weighing — and I can't risk paying him with a fake coin either!

His scales are simple balance scales, two pans in which coins can be placed, and either the pans balance, or one side drops while the other rises.

Oh — and no-one's willing to lend me a known good coin or coins to weigh against my coins. A very unfriendly place, this.

Finally, I don't even have a pencil or paper. I'm going to have to work this out without writing anything down...

How can I end up with nine good coins from my twelve, and at the same time manage to pay the miser with good coins for however many times I need to use his scales? No matter what I do, I obviously can't afford to use his scales more than twice...





If you post a solution, don't forget spoiler tags. Thanks!

Last edited by pdurrant; 06-14-2010 at 06:42 AM.
pdurrant is offline   Reply With Quote
Old 06-14-2010, 08:56 AM   #2
omk3
Wizard
omk3 can name that ebook in five wordsomk3 can name that ebook in five wordsomk3 can name that ebook in five wordsomk3 can name that ebook in five wordsomk3 can name that ebook in five wordsomk3 can name that ebook in five wordsomk3 can name that ebook in five wordsomk3 can name that ebook in five wordsomk3 can name that ebook in five wordsomk3 can name that ebook in five wordsomk3 can name that ebook in five words
 
omk3's Avatar
 
Posts: 1,454
Karma: 37243
Join Date: Dec 2009
Location: Europe
Device: pocketbook 360, kindle 4
Pdurrant, I'm enjoying your puzzles very much

Spoiler:
Let's see now.
I have twelve coins, so I can divide them into 4 groups of 3, A, B, C and D.

I put A and B on the scales.
If they don't have the same weight, the fake coin is in either A or B.
If they do, the fake coin is in either C or D.

If the fake coin is in either A or B, I weigh A with C.
If they have the same weight, the fake coin is in B.
If they don't have the same weight, the fake coin is in A.

If the fake coin is in either C or D, I weigh A with C again.
If they have the same weight, the fake coin is in D.
If they don't have the same weight, the fake coin is in C.

I have now identified a group of 3 coins, one of which is the fake one. I give all three to the miser, and he can work out for himself which one is the fake one and throw it away, he still gets 2 good coins for my use of the scales.
omk3 is offline   Reply With Quote
 
Enthusiast
Old 06-14-2010, 09:10 AM   #3
pdurrant
The Grand Mouse
pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.
 
pdurrant's Avatar
 
Posts: 31,712
Karma: 87828960
Join Date: Jul 2007
Location: Norfolk, England
Device: NOOK ST GlowLight
Quote:
Originally Posted by omk3 View Post
Pdurrant, I'm enjoying your puzzles very much
Yes, an excellent solution. You're good at this!
pdurrant is offline   Reply With Quote
Old 06-14-2010, 09:12 AM   #4
Catire
Lord of the Universe
Catire ought to be getting tired of karma fortunes by now.Catire ought to be getting tired of karma fortunes by now.Catire ought to be getting tired of karma fortunes by now.Catire ought to be getting tired of karma fortunes by now.Catire ought to be getting tired of karma fortunes by now.Catire ought to be getting tired of karma fortunes by now.Catire ought to be getting tired of karma fortunes by now.Catire ought to be getting tired of karma fortunes by now.Catire ought to be getting tired of karma fortunes by now.Catire ought to be getting tired of karma fortunes by now.Catire ought to be getting tired of karma fortunes by now.
 
Catire's Avatar
 
Posts: 648
Karma: 737849
Join Date: Jan 2008
Location: Maturin , Venezuela
Device: Sony Reader PRS-505 / PSP
Oops never mind I didn't read it before answering

Last edited by Catire; 06-14-2010 at 09:16 AM.
Catire is offline   Reply With Quote
Old 06-14-2010, 09:17 AM   #5
omk3
Wizard
omk3 can name that ebook in five wordsomk3 can name that ebook in five wordsomk3 can name that ebook in five wordsomk3 can name that ebook in five wordsomk3 can name that ebook in five wordsomk3 can name that ebook in five wordsomk3 can name that ebook in five wordsomk3 can name that ebook in five wordsomk3 can name that ebook in five wordsomk3 can name that ebook in five wordsomk3 can name that ebook in five words
 
omk3's Avatar
 
Posts: 1,454
Karma: 37243
Join Date: Dec 2009
Location: Europe
Device: pocketbook 360, kindle 4
Quote:
Originally Posted by Catire View Post
or

Spoiler:
Split the coins into 3 groups of 4 coins (A,B and C)

First you weigh A and B, if they have the same weight then the coin is in group C, if either of them weight more or less than the other then the coin is in that group. Discard the lighter or heavier coin groups.

You then split the group where the coin is into two groups of two and weigh them, wichever is heavier or lighter thats where the coin is. Discard the heavier or lighter group.

Then you just weigh the two coins left and you've found the fake one.
But:

Spoiler:
First, you used the scales more than two times.
Second, you say
Quote:
and weigh them, wichever is heavier or lighter thats where the coin is.
Obviously one is heavier, one is lighter. Which one has the fake coin? You don't know if the fake coin is lighter or heavier.


(Edit) Sorry, I answered before you deleted your solution...
omk3 is offline   Reply With Quote
Old 06-14-2010, 09:20 AM   #6
Catire
Lord of the Universe
Catire ought to be getting tired of karma fortunes by now.Catire ought to be getting tired of karma fortunes by now.Catire ought to be getting tired of karma fortunes by now.Catire ought to be getting tired of karma fortunes by now.Catire ought to be getting tired of karma fortunes by now.Catire ought to be getting tired of karma fortunes by now.Catire ought to be getting tired of karma fortunes by now.Catire ought to be getting tired of karma fortunes by now.Catire ought to be getting tired of karma fortunes by now.Catire ought to be getting tired of karma fortunes by now.Catire ought to be getting tired of karma fortunes by now.
 
Catire's Avatar
 
Posts: 648
Karma: 737849
Join Date: Jan 2008
Location: Maturin , Venezuela
Device: Sony Reader PRS-505 / PSP
Quote:
Originally Posted by omk3 View Post

(Edit) Sorry, I answered before you deleted your solution...
I immediatly thought of the "classic" one without bothering to read carefully
Catire is offline   Reply With Quote
Old 06-14-2010, 09:54 AM   #7
pdurrant
The Grand Mouse
pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.
 
pdurrant's Avatar
 
Posts: 31,712
Karma: 87828960
Join Date: Jul 2007
Location: Norfolk, England
Device: NOOK ST GlowLight
Quote:
Originally Posted by Catire View Post
I immediatly thought of the "classic" one without bothering to read carefully
Yes, slightly different constraints.
pdurrant is offline   Reply With Quote
Old 06-14-2010, 08:01 PM   #8
obs20
Wizard
obs20 ought to be getting tired of karma fortunes by now.obs20 ought to be getting tired of karma fortunes by now.obs20 ought to be getting tired of karma fortunes by now.obs20 ought to be getting tired of karma fortunes by now.obs20 ought to be getting tired of karma fortunes by now.obs20 ought to be getting tired of karma fortunes by now.obs20 ought to be getting tired of karma fortunes by now.obs20 ought to be getting tired of karma fortunes by now.obs20 ought to be getting tired of karma fortunes by now.obs20 ought to be getting tired of karma fortunes by now.obs20 ought to be getting tired of karma fortunes by now.
 
obs20's Avatar
 
Posts: 2,451
Karma: 26455224
Join Date: May 2010
Location: Florida
Device: Sony PRS 600, Nook ST, Toshiba Excite 10.1 AT 300
Okay here it goes:
Spoiler:

We need 9 good coins and 2 coins to pay the skinflint for the scale. We shouldn't get upset to offer him 3 coins of which 2 are good. Let him figure it out himself.

Put 3 coins on the left side of the scale.
Put 3 coins on the right side of the scale.
If the scale balances great we know that we have 6 good coins.
Then
Take 3 coins off the left side and replace them with 3 of the remaining coins.
If the scale balances great we have 9 good coins.
If not we know that the 3 remaining coins are good and we can use those.

If the scale didn't balance in the first place we still take 3 coins off the left side and replace them with three new coins. If the scale balances then all the coins on the scale are good and also the 3 remaining coins are good adding to 9.

If the scale still doesn't balance then we know that 1 of the 3 coins on the left are bad and we can use all the others to pay 9.
In either case we only uses the scale twice.
obs20 is offline   Reply With Quote
Old 06-14-2010, 08:03 PM   #9
obs20
Wizard
obs20 ought to be getting tired of karma fortunes by now.obs20 ought to be getting tired of karma fortunes by now.obs20 ought to be getting tired of karma fortunes by now.obs20 ought to be getting tired of karma fortunes by now.obs20 ought to be getting tired of karma fortunes by now.obs20 ought to be getting tired of karma fortunes by now.obs20 ought to be getting tired of karma fortunes by now.obs20 ought to be getting tired of karma fortunes by now.obs20 ought to be getting tired of karma fortunes by now.obs20 ought to be getting tired of karma fortunes by now.obs20 ought to be getting tired of karma fortunes by now.
 
obs20's Avatar
 
Posts: 2,451
Karma: 26455224
Join Date: May 2010
Location: Florida
Device: Sony PRS 600, Nook ST, Toshiba Excite 10.1 AT 300
Quote:
Originally Posted by omk3 View Post
Pdurrant, I'm enjoying your puzzles very much

Spoiler:
Let's see now.
I have twelve coins, so I can divide them into 4 groups of 3, A, B, C and D.

I put A and B on the scales.
If they don't have the same weight, the fake coin is in either A or B.
If they do, the fake coin is in either C or D.

If the fake coin is in either A or B, I weigh A with C.
If they have the same weight, the fake coin is in B.
If they don't have the same weight, the fake coin is in A.

If the fake coin is in either C or D, I weigh A with C again.
If they have the same weight, the fake coin is in D.
If they don't have the same weight, the fake coin is in C.

I have now identified a group of 3 coins, one of which is the fake one. I give all three to the miser, and he can work out for himself which one is the fake one and throw it away, he still gets 2 good coins for my use of the scales.
Way to go!
obs20 is offline   Reply With Quote
Old 06-15-2010, 02:14 AM   #10
dreams
It's about the umbrella
dreams ought to be getting tired of karma fortunes by now.dreams ought to be getting tired of karma fortunes by now.dreams ought to be getting tired of karma fortunes by now.dreams ought to be getting tired of karma fortunes by now.dreams ought to be getting tired of karma fortunes by now.dreams ought to be getting tired of karma fortunes by now.dreams ought to be getting tired of karma fortunes by now.dreams ought to be getting tired of karma fortunes by now.dreams ought to be getting tired of karma fortunes by now.dreams ought to be getting tired of karma fortunes by now.dreams ought to be getting tired of karma fortunes by now.
 
dreams's Avatar
 
Posts: 25,118
Karma: 56218156
Join Date: Jan 2009
Device: Sony 505| K Fire | KK 3G+Wi-Fi | iPhone 3Gs |Vista 32-bit Hm Prem w/FF
Here goes:
Spoiler:

Lt scale 5 - Rt scale 5 -- off to the Rt side 2

Scale is even so the fake is off to the side

Put those on scale to find the fake.

Pay miser 2 coins, toss the fake coin, and you keep 9 coins.

or if uneven..

L scale 5 - R scale 5 -- off to the R side 2

L scale is light, so put R scale bag to the side with other 2 coins

Then take one coin out of the L bag and put off to the Lt side

Now, L scale 2 - R scale 2 -- off to the Lt side 1

Scale is even so the coin off to the Lt side is fake

Pay the miser 2 coins, toss the fake coin, and you keep 9 coins.

or if uneven

L scale 2 - R scale 2 -- off to the Lt side 1

L side is light

Pay the miser 1 good coin from the Rt side and ask the miser if he wants the light L bag and he can weigh it himself to find the fake one?
dreams is offline   Reply With Quote
Old 06-15-2010, 03:02 AM   #11
pdurrant
The Grand Mouse
pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.
 
pdurrant's Avatar
 
Posts: 31,712
Karma: 87828960
Join Date: Jul 2007
Location: Norfolk, England
Device: NOOK ST GlowLight
Quote:
Originally Posted by obs20 View Post
Okay here it goes:
Yes, that's a good solution.
pdurrant is offline   Reply With Quote
Old 06-15-2010, 03:03 AM   #12
pdurrant
The Grand Mouse
pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.
 
pdurrant's Avatar
 
Posts: 31,712
Karma: 87828960
Join Date: Jul 2007
Location: Norfolk, England
Device: NOOK ST GlowLight
Quote:
Originally Posted by dreams View Post
Here goes:
Alas, you've missed the bit in the question that says "either slightly heavier or slightly lighter than the others" and have assumed that a fake coin will always be lighter than a real coin.

Try again? You're looking at it along the right sort of lines. And yes, it's acceptable to pay a debt of two coins with two good coins and one fake one.

Last edited by pdurrant; 06-15-2010 at 03:07 AM.
pdurrant is offline   Reply With Quote
Old 06-15-2010, 05:00 AM   #13
dreams
It's about the umbrella
dreams ought to be getting tired of karma fortunes by now.dreams ought to be getting tired of karma fortunes by now.dreams ought to be getting tired of karma fortunes by now.dreams ought to be getting tired of karma fortunes by now.dreams ought to be getting tired of karma fortunes by now.dreams ought to be getting tired of karma fortunes by now.dreams ought to be getting tired of karma fortunes by now.dreams ought to be getting tired of karma fortunes by now.dreams ought to be getting tired of karma fortunes by now.dreams ought to be getting tired of karma fortunes by now.dreams ought to be getting tired of karma fortunes by now.
 
dreams's Avatar
 
Posts: 25,118
Karma: 56218156
Join Date: Jan 2009
Device: Sony 505| K Fire | KK 3G+Wi-Fi | iPhone 3Gs |Vista 32-bit Hm Prem w/FF
And again

Spoiler:
Divide the coins into 4 bags. 3 coins in each bag =12

1- Weigh any 2 bags. If the same weight then remove one and add the 3rd bag to the scale.

2- If the 3rd bag:
  • weighs the same, then the fake is in the 4th bag. Pay the miser with the 4th bag.

****

1-Weigh any 2 bags. If uneven weight then remove either the lighter or heavier bag and add the 3rd bag to the scale.

2- If the 3rd bag:
  • weighs the same, then the fake is in the bag that was just removed. Pay the miser with that bag.
  • results in uneven, remove the bag that matches the weight of the first one removed (lighter or heavier) . The fake is in the bag still on the scale.


I give up. I have to be up in 4 1/2 hours and I am brain dead.
dreams is offline   Reply With Quote
Old 06-15-2010, 07:31 AM   #14
pdurrant
The Grand Mouse
pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.
 
pdurrant's Avatar
 
Posts: 31,712
Karma: 87828960
Join Date: Jul 2007
Location: Norfolk, England
Device: NOOK ST GlowLight
Quote:
Originally Posted by dreams View Post
And again

[solution]

I give up. I have to be up in 4 1/2 hours and I am brain dead.
Brain dead, but RIGHT! Congratulations.
pdurrant is offline   Reply With Quote
Old 06-15-2010, 07:32 AM   #15
pdurrant
The Grand Mouse
pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.pdurrant ought to be getting tired of karma fortunes by now.
 
pdurrant's Avatar
 
Posts: 31,712
Karma: 87828960
Join Date: Jul 2007
Location: Norfolk, England
Device: NOOK ST GlowLight
Quote:
Originally Posted by Catire View Post
I immediatly thought of the "classic" one without bothering to read carefully
You can still have another go — unless you've already checked one of the correct answers.
pdurrant is offline   Reply With Quote
Reply

Thread Tools Search this Thread
Search this Thread:

Advanced Search

Forum Jump

Similar Threads
Thread Thread Starter Forum Replies Last Post
iPad Twelve South Compass mini-review scottjl Apple Devices 1 07-27-2010 12:43 PM
Other Non-Fiction Chesterton, G K: Twelve Types, v1.2, 5 September 2009. Patricia Kindle Books 2 09-10-2009 04:34 PM
Other Non-Fiction Chesterton, G K: Twelve Types, v1, 5 September 2009. Patricia IMP Books 0 09-04-2009 11:01 PM
Twelve or so questions about the Kindle 2 enarchay Amazon Kindle 44 05-31-2009 12:22 PM


All times are GMT -4. The time now is 02:22 AM.


MobileRead.com is a privately owned, operated and funded community.