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January 23rd, 2013, 06:08 PM  #1 
Senior Member Joined: Dec 2012 Posts: 450 Thanks: 0  Cross+roads=danger????
Can any of you guys solve this alphanumeric puzzle? $\ \ \ \ $ CROSS + $\ \ \ \ $ ROADS $\ \ \ $_______ = DANGER $\ \ \ $_______ Each letter stands for a number.The value for each letter is same everywhere.The equation is absolutely true. Can anyone do this?Also please let me know the way you arrived at the solution. I had done this but by trial and error.It took about weeks.It was too much mind boggling.I hope someone can give simple solutions. Last edited by skipjack; August 15th, 2017 at 08:58 AM. 
January 23rd, 2013, 07:32 PM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,863 Thanks: 768  Re: CROSS+ROADS=DANGER????
3 solutions: 59488 + 64218 = 123706 90733 + 67513 = 158246 92344 + 83714 = 176058 Those are ALPHAMETICS, not alphanumerics. The "how to solve" is using a bit of logic, and some luck! For instance, you can tell right off the bat that g = 1; see that? And that d<>0. Here's a site where you can see a few examples: http://www.cadaeic.net/alphas.htm If you want more, google "alphametic puzzles". 
January 23rd, 2013, 10:28 PM  #3  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: CROSS+ROADS=DANGER???? Quote:
I don't understand your solutions, all 3 R's don't agree. Uh  Oh ... more LaTeX trouble.  
January 23rd, 2013, 11:25 PM  #4 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: CROSS+ROADS=DANGER????
I found $\displaystyle \ \ 96233$ $\displaystyle \ \ 62513$ $\displaystyle 158746$ D = 1 is obvious. From S + S = R we know R is even. Assume different letters stand for different numbers, then pick choices for R, S and O in that order. Took me about 40 minutes with pencil on paper. Last edited by skipjack; August 15th, 2017 at 09:03 AM. 
January 24th, 2013, 07:38 AM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,863 Thanks: 768  Re: CROSS+ROADS=DANGER????
My bad...assumed that ALL digits had to be used (hence the 0 also), and "innocently!" proceeded as such...our Agent's is right on! (took me 39 minutes) :P Well, if 1st word was by Elmer Fudd, then the R in CROSS would be a W: CWOSS and my solutions would work Wikipedia: Elmer Fudd speaks in an unusual way, replacing his Rs with Ws, so "Watch the road, Rabbit," is replaced with "Watch the woad, wabbit!" 
January 25th, 2013, 05:24 PM  #6  
Senior Member Joined: Dec 2012 Posts: 450 Thanks: 0  Re: CROSS+ROADS=DANGER???? Quote:
I was looking for a pure logical solution. Last edited by skipjack; August 15th, 2017 at 09:14 AM.  
August 15th, 2017, 08:07 AM  #7 
Newbie Joined: Aug 2017 From: Nepal Posts: 1 Thanks: 0  Solution
The answer is: $\ $ 96233 +62513  158746 Last edited by skipjack; August 15th, 2017 at 09:06 AM. 
August 15th, 2017, 09:21 AM  #8 
Global Moderator Joined: Dec 2006 Posts: 18,719 Thanks: 1536 
I posted this alphametic over nine years ago, but a solution wasn't posted then. I was given it to solve when I was aged 7 or 8  it took me about 20 minutes to find the answer.

August 15th, 2017, 11:54 AM  #9 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,863 Thanks: 768 
Can be arranged into this monster: 10000C + 10999R + 1100O + 12S  9900A  99990D  1000N  100G  10E = 0 ....which doesn't help much!! 
August 15th, 2017, 03:56 PM  #10 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,544 Thanks: 518 Math Focus: Yet to find out.  

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