wu :: forums
wu :: forums - integer grid

Welcome, Guest. Please Login or Register.
Sep 24th, 2018, 6:11am

RIDDLES SITE WRITE MATH! Home Home Help Help Search Search Members Members Login Login Register Register
   wu :: forums
   riddles
   hard
(Moderators: Icarus, Eigenray, towr, SMQ, Grimbal, william wu, ThudnBlunder)
   integer grid
« Previous topic | Next topic »
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print
   Author  Topic: integer grid  (Read 3368 times)
antkor
Newbie
*





   


Posts: 30
integer grid  
« on: Nov 29th, 2013, 10:05am »
Quote Quote Modify Modify

Make a grid consisting of 6 columns and 6 rows. In each one of the 36 cells that are formed, you must place a positive integer. Each positive integer must have all smaller positive integers in one of its' neighboring cells. For example, if you choose to place the number 3 inside a cell, then each numbers 1 and 2 must be in a cell that is up, down, left or right from 3 (the remaining two cells may contain any integers as long as these integers obey to the rules as well. diagonal cells do not count as neighboring cells.).
When you place all the 36 numbers inside, their sum must be exactly 93. Can you do it? (additional comment: 0 does not count as a positive integer, so you cannot use it.)
IP Logged
Grimbal
wu::riddles Moderator
Uberpuzzler
*****






   


Gender: male
Posts: 7408
Re: integer grid  
« Reply #1 on: Nov 30th, 2013, 3:00am »
Quote Quote Modify Modify

Looks like an IBM Ponder This problem
IP Logged
rmsgrey
Uberpuzzler
*****





134688278 134688278   rmsgrey   rmsgrey


Gender: male
Posts: 2818
Re: integer grid  
« Reply #2 on: Nov 30th, 2013, 7:09am »
Quote Quote Modify Modify

Immediate observations:
 
The average value in a cell must be a little over 2.5.
 
The largest integer you can use is 5, and it looks like you need to.
 
You can replace the problem with the equivalent one with non-negative integers (so you must have a 0 next to each larger number) and a target total of 57. It may or may not be easier to work with that version.
 
IP Logged
antkor
Newbie
*





   


Posts: 30
Re: integer grid  
« Reply #3 on: Dec 1st, 2013, 6:53am »
Quote Quote Modify Modify

rmsgrey is correct about what he says. Although, i am not aware of the variation he suggests. The challenge is of course to create the grid. I have managed to do it, but up to now i am breaking the rule once. I haven't managed to solve it perfectly, even though I am pretty sure it can be done. I am not aware of any logical way that gives the answer, so I suspect the only way of solving it is to brute force it.
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