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June 27th, 2016, 11:10 AM  #1 
Newbie Joined: Jun 2016 From: baku Posts: 1 Thanks: 0  Problem involving cubed numbers
ABCD  DCBA = A^3 + B^3 + C^3 + D^3 ABCD and DCBA are four digit numbers. A, B, C, D are different numbers between 0 and 9. 
June 28th, 2016, 04:50 AM  #2 
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551 
You really did not ask a question. Do you want the answer (which we tend not to give for homework) or help finding the answer. If the latter, this kind of problem teaches you how to use information that is general knowledge but not explicit in the statement of the problem or that is implied but not obvious from the problem itself. Where I would start is with this: a, b, c, and d are nonnegative. And we are dealing with FOUR digit numbers. So a and d are greater than 0. Do you see why? So $a^3 + b^3 + c^3 + d^3 > 0 \implies d \not > a.$ Why? But the problem says a and d are not equal so $1 \le d < a \le 9.$ What thoughts do you have about what to try next? 
June 28th, 2016, 06:13 AM  #3 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,150 Thanks: 730 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
Here's another hint for problems like this: if ABCD is a fourdigit number where the digits have been replaced with letters, then an equivalent description of the number is $\displaystyle 1000A + 100B + 10C + D$ where A, B, C and D are now algebraic variables (and also integers). 
June 28th, 2016, 11:24 AM  #4  
Banned Camp Joined: Jun 2014 From: Earth Posts: 945 Thanks: 191  Quote:
                                                                  As another true example, there was a sign on a wall in a Kroger supermarket deli that read: "No sugar cookies are here!" I asked a worker, "When will the sugar cookies be here?" The hyphen makes all the difference.  
June 28th, 2016, 12:42 PM  #5  
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551  Quote:
 
June 28th, 2016, 07:56 PM  #6 
Banned Camp Joined: Jun 2014 From: Earth Posts: 945 Thanks: 191  
June 29th, 2016, 01:23 AM  #7  
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,150 Thanks: 730 Math Focus: Physics, mathematical modelling, numerical and computational solutions  Quote:
Hint... look up the meaning of the word "pedantry"  

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