CTK Exchange
Front Page
Movie shortcuts
Personal info
Awards
Reciprocal links
Terms of use
Privacy Policy

Interactive Activities

Cut The Knot!
MSET99 Talk
Games & Puzzles
Arithmetic/Algebra
Geometry
Probability
Eye Opener
Analog Gadgets
Inventor's Paradox
Did you know?...
Proofs
Math as Language
Things Impossible
My Logo
Math Poll
Other Math sit's
Guest book
News sit's

Recommend this site
Manifesto: what CTK is about |Store| Search CTK Buying a book is a commitment to learning Table of content Things you can find on CTK Chronology of updates Email to Cut The Knot Recommend this page

CTK Exchange

Subject: "can this be done?"     Previous Topic | Next Topic
Printer-friendly copy     Email this topic to a friend    
Conferences The CTK Exchange High school Topic #244
Reading Topic #244
dinamo_007
Member since Jun-23-03
 Jun-23-03, 05:16 PM (EST)
Click to send private message to dinamo_007 Click to add this user to your buddy list  
"can this be done?"
 
   There are 20 objects on the left side. They all need to be past on to the right side in five days. At least one per day, no even numbers, counting numbers only. How do I do this?

Attachments
https://www.cut-the-knot.org/htdocs/dcforum/User_files/Myfriendsaysthereisasolution
https://www.cut-the-knot.org/htdocs/dcforum/User_files/isthereonereally

  Alert | IP Printer-friendly page | Edit | Reply | Reply With Quote | Top
Graham C
Member since Feb-5-03
 Jun-24-03, 09:15 AM (EST)
Click to EMail Graham%20C Click to send private message to Graham%20C Click to view user profileClick to add this user to your buddy list  
1. "RE: can this be done?"
In response to message #0
 
   I can't access either file, so don't know what the problem is.


  Alert | IP Printer-friendly page | Edit | Reply | Reply With Quote | Top
Michael Klipper
guest
 Jun-25-03, 01:13 PM (EST)
 
2. "RE: can this be done?"
In response to message #0
 
   Your attachments don't really load, but I think I know what the question is. If you start with twenty objects on one side of a door, and then each day you send a positive odd number of objects through the door to the other side, then can all the objects go through in five days?

I believe this is the question. The answer is that it is not possible, since the sum of five odd numbers can never be even. So if t1, t2, t3, t4, and t5 are your five totals, it is impossible for them all to be even and yet satisfy
t1 + t2 + t3 + t4 + t5 = 20

Michael


  Alert | IP Printer-friendly page | Edit | Reply | Reply With Quote | Top
Rod H.
guest
 Jun-26-03, 09:58 AM (EST)
 
3. "RE: can this be done?"
In response to message #2
 
   I agree, 5 positive odd numbers will always add up to an odd number, however, could there be a trick involved? Perhaps one could move an odd number back to the left on one of the days.
i.e.
day 1 -> 5
day 2 -> 5
day 3 -> 5
day 4 -> 3; <- 1
day 5 -> 3.

There doesn't appear to be any constraint prohibiting this, so you have to keep an open mind!


  Alert | IP Printer-friendly page | Edit | Reply | Reply With Quote | Top
sambasivan
guest
 Jun-27-03, 03:56 PM (EST)
 
4. "RE: can this be done?"
In response to message #0
 
   this is not possible since the sum of five odd numbers is always an odd number (proof is very simple : every sum of two odd numbers is an even number, sum of two even numbers is always even and sum of odd and an even number is always odd)

hence 20 cannot be broken into five odd numbers. there is no solution possible for this problem


  Alert | IP Printer-friendly page | Edit | Reply | Reply With Quote | Top

Conferences | Forums | Topics | Previous Topic | Next Topic

You may be curious to have a look at the old CTK Exchange archive.
Please do not post there.

|Front page| |Contents|

Copyright © 1996-2018 Alexander Bogomolny

73186864