the sum of a two digit number and the number obtained by reversing its digits is a square number.how many such numbers a re there??

• 8 Numbers
  
  Let the two digit number= (10x+y), then number obtained by reversing its digit=(10y+x)
  Sum of these two numbers=(10x+y) + (10y+x) = 11(x+y)
  The square number multiple of 11 is 121, where x,y lies between 1 and 9.
  For 11(x+y)= 121, (x,y)=(2,9) (3,8) (4,7) (5,6) (6,5) (7,4) (8,3) (9,2) total 8 combinations.
  So we can have 8 such numbers 29, 38, 47, 56, 65, 74, 83 and 92.
• 7 years agoHelpfull: Yes(32) No(1)
• Let 2 digit no.=xy Where x,y are digits from 0 to 9
  Reverse of no.=yx
  According to question
  Sum of no.+sum of reverse of no.=square of any no.
  10x+y+10y+x=square
  11*(x+y)=square
  1
• 7 years agoHelpfull: Yes(0) No(12)