August 23rd, 2013, 06:06 AM  #1 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,419 Thanks: 1025  Math Q&A challenge (Part 11)
You have an integer number where any digit appears at most twice. The sum of all neighboring four digits in this number is a square. Example: 205290 is such a number because no digit appears more than twice, and 2+0+5+2, 0+5+2+9, and 5+2+9+0 are squares. What is the maximum possible value for this number? 
August 24th, 2013, 02:34 PM  #2 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Math Q&A challenge (Part 11)
This is interesting , I'll make the frst submission. How about 9880013571357 ? 
August 24th, 2013, 07:03 PM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,419 Thanks: 1025  Re: Math Q&A challenge (Part 11)
Good try Agent...there is a higher number.

August 24th, 2013, 07:37 PM  #4  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Math Q&A challenge (Part 11) Quote:
 
August 24th, 2013, 08:09 PM  #5 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Math Q&A challenge (Part 11) 
August 24th, 2013, 08:13 PM  #6 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,419 Thanks: 1025  Re: Math Q&A challenge (Part 11)
Looked at both links. What do I not see? 
August 24th, 2013, 08:30 PM  #7 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Math Q&A challenge (Part 11)
CRG gave me a 'ribbing' using Mario so I countered with Wario... you have to know about video game plumbers ... and bizzarro characters of a stienfool universe ... Don't worry, you didn't miss anything important. I tried a few more but can't get a bigger number. 
August 24th, 2013, 10:17 PM  #8 
Global Moderator Joined: Dec 2006 Posts: 20,655 Thanks: 2087 
81978100367936

August 24th, 2013, 10:23 PM  #9  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Math Q&A challenge (Part 11) Quote:
By the way, skipjack, if you don't have any question to ask then just pass it to someone for the game to continue, ok?  
August 24th, 2013, 10:44 PM  #10 
Senior Member Joined: Sep 2012 From: British Columbia, Canada Posts: 764 Thanks: 53  Re: Math Q&A challenge (Part 11)
And it looks like we forgot to post the rules AGAIN. :P 

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