could any one give clear explaination on the problems of crypto arithmetic,,,,plz solve this problem with detailed explaination.....banana+guava=orange.what is the value of o+r+a+n+g+e

• BANANA
  +GUAVA
  -------
  ORANGE
  -------
  
  means A+A=E, N+V=G, A+A=N, N+U=A, A+G=R, B+_=O
  
  So just start from last
  A+A=E
  "A" can have d values ranging {0,1,2,3,4,5,6,7,8,9}
  first lets take A=0... A+A= 0+0=0... Again d result is 0... means E=0... So not possible for 2 alphabets to have same number...
  
  Lets take A=1... A+A= 1+1=2... A=1, E=2,... v have to find d value for "N"...
  Look A+A=N (3rd term)... A+A is already "E" (ie E=2A)... So definitely N should not be 2A... Therefore N=2A+1... There should be remainder from the 2nd term...
  so N=2A+1... N=2(1)+1= 3... Assign a value for to get a remainder... Take V=7
  3+7=0 carry 1... 1+A+A=3...
  next N+U=A...result should be 1... 3+8=1 carry 1...
  next A+G=R... 1+1+7=9... There is no carry which means B nd O ll have d same value... so not possible... So try for different values...
  Note here A+G=R should produce a carry... then only v can yield B+carry=O
  
  By trial nd error method, Again start from last... Try A=2... Its also not possible... Agan A=3... Not possible...
  Now A=4... E=2A=8... N=2A+1=9...
  For getting a carry If i take V=1, A+G ll not produce carry... So take V=2... N+V=G... 9+2=1 carry 1... 1+A+A=9... N+U should produce 4... 9+5=4 so U=5... next A+G = 4+1=5 not producing carry... Here 4+(>5) only yields a carry...
  So v should get G value >5...
  So again trail nd error method, N+V=G... Lets take V=7 ..N+V=G... 9+7=6 carry 1...
  1+A+A=N... N+U=A... 9+5=4 carry 1... 1+A+G=R... 1+4+6=1 carry 1... 1+B+_=O...
  Values remaining is {0,2,3}
  1+0+_=1 not possible
  1+2+_=3
  
  
  So
  B=2, A=4, N=9, A=4, N=9, A=4
  G=6, U=5, A=4, V=7, A=4
  O=3, R=1, A=4, N=9, G=6, E=8
  
  O + R + A + N + G + E
  3 + 1 + 4 + 9 + 6 + 8 = 31
  
  Ans : 31
• 10 years agoHelpfull: Yes(88) No(2)
• @IAMATURE
  
  Its Assign a value for "V" to get a remainder...
  bcozzz already A+A=E... So definitely A+A should not be equal to N... So N+V should produce a carry... So A+A+1=N... (ie N=E+1)... Now we have to assign a value for V to get a carry...
  
  I hope u understand this...
  
  
• 10 years agoHelpfull: Yes(6) No(1)
• Is there any other method to solve it quickly?
• 10 years agoHelpfull: Yes(2) No(3)
• B A N A N A+
  - G U A V A
  -------------
  O R A N G E
  
  ===>
  A+A = E
  A+A+1 = E+1 = N
  B+1 = O
  A+G =R and carry 1
  and B,O,A not equal to zero
  for A
• 10 years agoHelpfull: Yes(1) No(4)
• i am new for crypto......i did not understand this procedre.plz explain me in a clear manner i am basic learner for crypto i hope as early as possible...
• 10 years agoHelpfull: Yes(1) No(0)
• 31
  by adding banana and guava
  we get 314968=31
• 10 years agoHelpfull: Yes(0) No(0)
• @ Saraswathy:
  I did not understand this line :
  Assign a value for to get a remainder... Take V=7
  3+7=0 carry 1... 1+A+A=3...
  
  
• 10 years agoHelpfull: Yes(0) No(0)
• thanx alot sarawathy 4r this explaination....
  
• 10 years agoHelpfull: Yes(0) No(0)
• to all kindly tell wats wrong in
  B A N A N A
  4 8 7 8 7 8
  G U A V A
  + 3 0 8 5 8
  ------------------------
  O R A N G E
  5 1 8 7 3 6
  
  
  PLZ DO REPLY IF SEE IT
• 10 years agoHelpfull: Yes(0) No(2)
• ne mre ans is also possible by this methd and that ans is:
  287878
  +40868
  -----------
  328746
  
  
  3+2+8+7+4+6=30
• 10 years agoHelpfull: Yes(0) No(0)