wu :: forums
wu :: forums - Stamps and envelopes

Welcome, Guest. Please Login or Register.
Sep 25th, 2018, 10:26am

RIDDLES SITE WRITE MATH! Home Home Help Help Search Search Members Members Login Login Register Register
   wu :: forums
   riddles
   medium
(Moderators: Grimbal, Icarus, Eigenray, towr, ThudnBlunder, william wu, SMQ)
   Stamps and envelopes
« Previous topic | Next topic »
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print
   Author  Topic: Stamps and envelopes  (Read 1071 times)
Altamira_64
Junior Member
**





   


Posts: 116
Stamps and envelopes  
« on: Jan 2nd, 2016, 7:10am »
Quote Quote Modify Modify

We have 14 different lots of stamps, each lot from a different country (all stamps of each lot are the same) and an adequate number of envelopes.  
We must place exactly 4 different stamps on each envelope. What is the maximum number of envelopes we can make, provided that any two envelopes must not have more than one stamp in common?
« Last Edit: Jan 3rd, 2016, 7:18am by Altamira_64 » IP Logged
markr
Junior Member
**





   


Gender: male
Posts: 90
Re: Stamps and envelopes  
« Reply #1 on: Jan 3rd, 2016, 11:43am »
Quote Quote Modify Modify

Each lot can go on at most floor((14-1)/3) = 4 envelopes.  With 13 lots, you can get to the theoretical maximum 13 envelopes.  I'm not sure that an extra lot allows you to get to a 14th envelope.  I'm guessing not.
IP Logged
Altamira_64
Junior Member
**





   


Posts: 116
Re: Stamps and envelopes  
« Reply #2 on: Jan 7th, 2016, 12:36pm »
Quote Quote Modify Modify

the stamps from each lot can be used multiple times.
IP Logged
rmsgrey
Uberpuzzler
*****





134688278 134688278   rmsgrey   rmsgrey


Gender: male
Posts: 2818
Re: Stamps and envelopes  
« Reply #3 on: Jan 8th, 2016, 1:15pm »
Quote Quote Modify Modify

on Jan 7th, 2016, 12:36pm, Altamira_64 wrote:
the stamps from each lot can be used multiple times.

 
That doesn't seem relevant to markr's post.
 
Label the stamp lots A-N for convenience of reference.
 
Every time you use an A stamp, it has to go with 3 different stamps - so you can put ABCD, AEFG, AHIJ, AKLM, but then you can't use A again because with only N that it hasn't been used with, there aren't enough new lots of stamps to go with it.
 
That means each stamp lot can be used at most 4 times (with 12 of the other 13 lots) so the maximum possible number of envelopes is 14 lots times 4 stamps per lot, divided by 4 stamps per envelope for a total of 14 as the upper bound.
 
13 envelopes is achievable (and can be achieved only using 13 lots), which gives a lower bound, so the open question is whether you can actually get the 14th envelope or not.
 
My intuition returns a solid "maybe".
IP Logged
dudiobugtron
Uberpuzzler
*****





   


Posts: 713
Re: Stamps and envelopes  
« Reply #4 on: May 3rd, 2016, 11:45pm »
Quote Quote Modify Modify

Solution for 13, in case it is useful for other solvers:
ABCD
AEFG
AHIJ
AKLM
BEHK
BFIL
BGJM
CEIM
CFJK
CGHL
DEJL
DGIK
DFHM
IP Logged
Altamira_64
Junior Member
**





   


Posts: 116
Re: Stamps and envelopes  
« Reply #5 on: May 12th, 2016, 12:40am »
Quote Quote Modify Modify

Solution with 14:
 
ACFG
BDGH
CEHI
DFIJ
EGJK
FHKL
GILM
HJMN
IKNA
JLAB
KMBC
LNCD
MADE
NBEF
IP Logged
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print

« Previous topic | Next topic »

Powered by YaBB 1 Gold - SP 1.4!
Forum software copyright 2000-2004 Yet another Bulletin Board