Find integers a, b & c - of course, if you can!

Replies

• 

  Differential

  Can "C" be more than 1 digit number ?
• 

  Kaustubh Katdare

  I don't know, seriously.
• 

  nishank_eureka

  put three for loops each iterating from 0 to 9 and check the condition above.
  Manually i dont think i can find it.
  
  Here is the programme.
  Disclaimer: The synatx may not be proper.
  
  for(a=0;a<=9;a++)
  {
  for(b=0;b<=9;b++)
  {
  for(c=0;c<=9;c++)
  {
  int a1 = 9876543210 + a;
  int a2 =1234567890 + b;
  int cube = Math.pow((a+b+c),3);
  int Sum = a1 + a2;
  int result = a1.compareTo(a2);
  if (result ==0)
  {
  syso(a,b,c);
  }else
  continue;
  }
  }
  }
• 

  electron1212

  450 * 987654321 + 4500 * 123456789 + 5050 = (450+4500+5050) ^ 3 = 1000000000000
  
  7350 * 987654321 + 6000 * 123456789 + 6650 = (7350+6000+6650) ^ 3 = 8000000000000
  
  but what is the trick ???😕
• 

  Fazil

  My Program found 4 results. First three found with in 1 Min 48 seconds. Total scan took 7 Min 19 seconds.
  
  Result:
  {0, 0, 1} - 0 Sec
  {450, 4500, 5050} - 6 Sec
  {7350, 6000, 6650} - 1 Min 48 Sec
  {27150, 1500, 1350} - 6 Min 24 Sec
  
  Program:
  void main()
  {
  unsigned long double LHS, RHS, Duration;
  int a, b, c, Left, Right;
  time_t Start, Stop;
  
  time( &Start );
  for( a = 0; a < 31427; a++ )
  {
  for( b = 0; b < 31427; b++ )
  {
  Left = 0;
  Right = 31428;
  
  while( Left < ( Right - 1 ))
  {
  c = ( Left + Right ) / 2;
  
  LHS = unsigned long double(a) * 987654321;
  LHS += unsigned long double(b) * 123456789;
  LHS += unsigned long double(c);
  
  RHS = unsigned long double( a + b + c );
  RHS = RHS * RHS * RHS;
  
  if( LHS == RHS )
  {
  printf("\n\n987654321*%d + 123456789*%d + %d = %.0Lf\n", a, b, c, LHS);
  printf("(%d + %d + %d)^3 = %.0Lf\n", a, b, c, RHS);
  printf("987654321*%d + 123456789*%d + %d = (%d + %d + %d)^3\n\n", a, b, c, a, b, c);
  break;
  }
  if( LHS < RHS )
  {
  Right = c;
  }
  else
  {
  Left = c;
  }
  }
  }
  time( &Stop );
  Duration = difftime( Stop, Start );
  int Seconds = (int)fmod( Duration, 60 );
  int Minutes = (int)fmod( floor(Duration / 60), 60 );
  int Hours = int(Duration / 3600);
  
  printf("\rCompleted:%0.1Lf%%", (a * 100.) / 31427);
  printf("\tElapsed Time:%02d:%02d:%02d", Hours, Minutes, Seconds);
  }
  }
  
  Output:
  987654321*0 + 123456789*0 + 1 = 1
  (0 + 0 + 1)^3 = 1
  987654321*0 + 123456789*0 + 1 = (0 + 0 + 1)^3
  
  Completed:1.4% Elapsed Time:00:00:06
  
  987654321*450 + 123456789*4500 + 5050 = 1000000000000
  (450 + 4500 + 5050)^3 = 1000000000000
  987654321*450 + 123456789*4500 + 5050 = (450 + 4500 + 5050)^3
  
  Completed:23.4% Elapsed Time:00:01:48
  
  987654321*7350 + 123456789*6000 + 6650 = 8000000000000
  (7350 + 6000 + 6650)^3 = 8000000000000
  987654321*7350 + 123456789*6000 + 6650 = (7350 + 6000 + 6650)^3
  
  Completed:86.4% Elapsed Time:00:06:24
  
  987654321*27150 + 123456789*1500 + 1350 = 27000000000000
  (27150 + 1500 + 1350)^3 = 27000000000000
  987654321*27150 + 123456789*1500 + 1350 = (27150 + 1500 + 1350)^3
  
  Completed:100.0% Elapsed Time:00:07:19
• 

  Saandeep Sreerambatla

  Superb Solution Fazil.