
Math General Math Forum  For general math related discussion and news 
 LinkBack  Thread Tools  Display Modes 
January 31st, 2015, 06:48 PM  #1 
Member Joined: Jan 2015 From: Orlando, Florida Posts: 92 Thanks: 10  Can you do this without a complete bash?
If abcd = (ab+cd)^2 and c is the only digit that can be 0, find the sum of all possible abcd. Note that abcd is a four digit number, not a*b*c*d (same with ab and cd, but they are 2 digit numbers). Last edited by skipjack; February 1st, 2015 at 09:10 AM. 
February 1st, 2015, 09:50 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,547 Thanks: 1752 
Start by considering possible values of a. There are very few candidates. As only c can be zero, abcd = 3025 is ruled out. 
February 1st, 2015, 11:05 AM  #3 
Member Joined: Jan 2015 From: Orlando, Florida Posts: 92 Thanks: 10 
but how will you be able to tell that a number abcd works without testing it (i.e. squaring)? can you eliminate some squares right away (besides the one that have b=0 or d=0) like 46^2 for example? (without squaring 46 and seeing if ab+cd=46) 
February 1st, 2015, 04:50 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 19,547 Thanks: 1752 
As abcd = (ab + cd)², its digital root is 1 or 9. As (ab + cd)² ends in d, bd = 81, 44, 49, 84, 86 or 89. As (ab + cd)² begins with a, if a < 5, c = 1 or 2, if a = 5 or 6, c = 1, if a = 7, c = 0 or 1, and if a = 8 or 9, c = 0. (The above deductions about c require knowledge of some squares or square roots.) The above leaves less than ten possible values for ab + cd, and 46 isn't one of them. 

Tags 
bash, complete, number, problem, theory 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
complete  mared  Algebra  16  November 17th, 2014 12:01 PM 
Complete the Square  tallbabe1  Algebra  1  December 15th, 2012 04:50 PM 
NPComplete question  complexity9  Computer Science  0  December 5th, 2011 03:44 AM 
How I can complete my answer ?  rsoy  Calculus  2  December 28th, 2010 10:18 AM 
How I complete this question ..  rsoy  Algebra  3  February 15th, 2010 02:26 AM 