mersenneforum.org  

Go Back   mersenneforum.org > Fun Stuff > Puzzles

Reply
 
Thread Tools
Old 2016-07-31, 16:37   #1
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

266116 Posts
Default Avgvst 2016

https://www.research.ibm.com/haifa/p...ugust2016.html
Batalov is offline   Reply With Quote
Old 2016-07-31, 19:12   #2
a1call
 
a1call's Avatar
 
"Rashid Naimi"
Oct 2015
Remote to Here/There

2×19×59 Posts
Default

That does not make sense. The wording implies that the scale is not a balance scale.
With a single Measurment reading for 10 bags any Measurment not involving any of the 10 bags will leave unmeasured bags unknown. If all 10 bags are measured at once then there would be no way to distinguish between them. The best you could do is to determine the number of counterfeit bags but not to know which specific bags are counterfeit.

BTW There seem to be a typo (or two) in the title or am I missing something.

Last fiddled with by a1call on 2016-07-31 at 19:17
a1call is offline   Reply With Quote
Old 2016-07-31, 19:42   #3
firejuggler
 
firejuggler's Avatar
 
"Vincent"
Apr 2010
Over the rainbow

2·3·11·43 Posts
Default

The wording imply a scale with 2 plate.
firejuggler is offline   Reply With Quote
Old 2016-07-31, 19:43   #4
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

3×52×131 Posts
Default

Quote:
Originally Posted by a1call View Post
... or am I missing something.
That one.
Batalov is offline   Reply With Quote
Old 2016-07-31, 19:47   #5
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

3×52×131 Posts
Default

Quote:
Originally Posted by Ponder This
...using a single measurement with an accurate weighing scale.
LMGTFY ... "an accurate weighing scale" -->
Attached Thumbnails
Click image for larger version

Name:	pce-instruments-accurate-scale.jpg
Views:	146
Size:	4.1 KB
ID:	14714  
Batalov is offline   Reply With Quote
Old 2016-07-31, 20:09   #6
firejuggler
 
firejuggler's Avatar
 
"Vincent"
Apr 2010
Over the rainbow

2·3·11·43 Posts
Default

ah, this *accurate scale* has a limit?
firejuggler is offline   Reply With Quote
Old 2016-07-31, 20:35   #7
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

231418 Posts
Default

None is implied by PT, but it is clear that within this problem a 20.470 kg limit will do fine, with precision of 1 g.
Such scales are quite routine. Our labs have scales that are doing a few grams but up to the fifth, I think, decimal digit behind dot, so they are more precise.
Batalov is offline   Reply With Quote
Old 2016-08-01, 02:48   #8
a1call
 
a1call's Avatar
 
"Rashid Naimi"
Oct 2015
Remote to Here/There

224210 Posts
Default

The problem implies that for N<1024 it would take more than a single Measurment to solve. So the actual problem would require more than a single Measurment and no maximum is specified which makes the solution trivial. The problem is the N>=1024 being solved in a single Measurment does not make sense specially with an unknown number of fake coin bags.
I just don't understand the parameters of the problem.
a1call is offline   Reply With Quote
Old 2016-08-01, 03:20   #9
LaurV
Romulan Interpreter
 
LaurV's Avatar
 
"name field"
Jun 2011
Thailand

2×17×293 Posts
Default

The 1024 is just an example, same as they use to give every month examples, for every challenge. It does not imply that you would need more measurements if N is smaller. It may be true or not, but the example itself implies nothing. Of course, we learned in elementary school how to solve the "example". In fact, the condition is very weak, even if N>=512, you could do it with a single scale very simply, you take 2^(n-1) coins from the n-th bag, and you have only 10 bags... So you don't need N >= 1024. When N>=512, you could take 1 coin from the first bag, 2 from the second, 4 from the third, etc, and 512 from the 10th bag, then you scale them together. At the end you have 1023 coins and expect to get 10230 grams if all coins are good, but you will get less. You get one gram less for each bad coin. Write the difference in binary and you know exactly how many bags have wrong coins, and which bags they are. If for example you get 29 grams less, which in binary is 11101, you know that there are 4 bags with bad coins, and those are the first, the third, forth and fifth.

Now, you have less coins in each bag. But you also know that there are at most 3 bags with bad coins. So, it should not be difficult to devise a scheme where you can point to the cheating bags, with only one scaling.

This problem, same like the one last month, is actually very nice.

Last fiddled with by LaurV on 2016-08-01 at 03:49
LaurV is offline   Reply With Quote
Old 2016-08-01, 03:28   #10
a1call
 
a1call's Avatar
 
"Rashid Naimi"
Oct 2015
Remote to Here/There

43028 Posts
Default

Thank you LaurV,
Somehow I was under the impression that bags where to be weighted and not the coins.
The example does make sense now.
Thanks again for the clarification.
a1call is offline   Reply With Quote
Old 2016-08-04, 19:15   #11
R. Gerbicz
 
R. Gerbicz's Avatar
 
"Robert Gerbicz"
Oct 2005
Hungary

110001000002 Posts
Default

New update:

"Update (4/8): To get a '**' find a solution for the minimal N."
R. Gerbicz is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
July 2016 Xyzzy Puzzles 4 2016-08-06 22:51
June 2016 Xyzzy Puzzles 16 2016-07-07 02:51
EM 2016 Cybertronic Soap Box 1 2016-06-26 21:03
May 2016 Xyzzy Puzzles 6 2016-06-06 19:02
April 2016 Xyzzy Puzzles 10 2016-05-05 05:42

All times are UTC. The time now is 12:40.


Mon May 23 12:40:53 UTC 2022 up 39 days, 10:42, 0 users, load averages: 1.59, 1.64, 1.72

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2022, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.

≠ ± ∓ ÷ × · − √ ‰ ⊗ ⊕ ⊖ ⊘ ⊙ ≤ ≥ ≦ ≧ ≨ ≩ ≺ ≻ ≼ ≽ ⊏ ⊐ ⊑ ⊒ ² ³ °
∠ ∟ ° ≅ ~ ‖ ⟂ ⫛
≡ ≜ ≈ ∝ ∞ ≪ ≫ ⌊⌋ ⌈⌉ ∘ ∏ ∐ ∑ ∧ ∨ ∩ ∪ ⨀ ⊕ ⊗ 𝖕 𝖖 𝖗 ⊲ ⊳
∅ ∖ ∁ ↦ ↣ ∩ ∪ ⊆ ⊂ ⊄ ⊊ ⊇ ⊃ ⊅ ⊋ ⊖ ∈ ∉ ∋ ∌ ℕ ℤ ℚ ℝ ℂ ℵ ℶ ℷ ℸ 𝓟
¬ ∨ ∧ ⊕ → ← ⇒ ⇐ ⇔ ∀ ∃ ∄ ∴ ∵ ⊤ ⊥ ⊢ ⊨ ⫤ ⊣ … ⋯ ⋮ ⋰ ⋱
∫ ∬ ∭ ∮ ∯ ∰ ∇ ∆ δ ∂ ℱ ℒ ℓ
𝛢𝛼 𝛣𝛽 𝛤𝛾 𝛥𝛿 𝛦𝜀𝜖 𝛧𝜁 𝛨𝜂 𝛩𝜃𝜗 𝛪𝜄 𝛫𝜅 𝛬𝜆 𝛭𝜇 𝛮𝜈 𝛯𝜉 𝛰𝜊 𝛱𝜋 𝛲𝜌 𝛴𝜎𝜍 𝛵𝜏 𝛶𝜐 𝛷𝜙𝜑 𝛸𝜒 𝛹𝜓 𝛺𝜔