My Math Forum  

Go Back   My Math Forum > High School Math Forum > Probability and Statistics

Probability and Statistics Basic Probability and Statistics Math Forum


Reply
 
LinkBack Thread Tools Display Modes
September 13th, 2015, 11:21 AM   #1
Banned Camp
 
Joined: Dec 2013

Posts: 1,117
Thanks: 41

Hard puzzle

We have 252 5-uples extracted from 10 numbers (1 to 10).
C(10,5)=252
We want to place them under constraint around a circular table.

Definition 1 :

Two 5-uples are called brothers if they share 4 numbers.
Example : 1-2-3-4-5 and 1-2-3-4-10 are brothers.
Each 5-uple has 25 brothers (C(5,4)*(C(5,1)).
Brotherhood is not transitive :
A=1-2-3-4-5
B=1-2-3-4-6
C=1-2-3-6-7

A is brother of B but not brother of C
B is brother of A and brother of C
C is brother of B but not of A

Definition 2 :

We call distance d the number of seats at left and at right of some 5-uple sitting around the table.

Example : d=5
We count 5 seats at left and 5 seats at right of a sitting 5-uple.

The challenge is to place all the 252 5-uples around a circular table such as if we choose any 5-uple no brother will be sitting at the distance d with d maximal.

Example : if the maximal value is 8 then any 5-uple out of the 252 will NOT have a brother sitting at the distance 8.

What is the value of d?
What are the seats choosen for the 252 5-uples or in other words how are they going to be placed?
mobel is offline  
 
September 14th, 2015, 03:47 PM   #2
Banned Camp
 
Joined: Dec 2013

Posts: 1,117
Thanks: 41

Almost solved!
Without computer...
mobel is offline  
Reply

  My Math Forum > High School Math Forum > Probability and Statistics

Tags
hard, puzzle



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Puzzle Denis New Users 13 March 11th, 2013 04:20 PM
New Puzzle johnr New Users 13 February 20th, 2013 03:36 PM
Try this puzzle mathmaniac New Users 29 February 17th, 2013 07:24 PM
Try this puzzle mathmaniac Applied Math 0 December 31st, 1969 04:00 PM





Copyright © 2019 My Math Forum. All rights reserved.