In between 2000 and 2199 how many numbers are there who are perfect square?? (like 2194=2+1+9+4=16 which is a perfect square)

• from 2000 to 2099 => 20xy
  sum of 1st two digit is 2, for no. to be perfect square (x+y)= 2,7,14
  x+y=2, (x,y)=(0,2),(2,0),(1,1) => 3 no.s
  x+y=7, (x,y)= (0,7),(1,6),...,(7,0) => 8 no.s
  x+y=14, (x,y)= (5,9),(6,8),(7,7),(8,6),(9,5) => 5 no.s
  
  from 2100 to 2199 => 21xy
  sum of 1st two digit is 3, for no. to be perfect square (x+y)= 1,6,13
  x+y=1, (x,y)=(0,1),(1,0) => 2 no.s
  x+y=6, (x,y)=(0,6),(1,5),...,(6,0) => 7 no.s
  x+y=13, (x,y)=(4,9),(5,8),...,(9,4) => 6 no.s
  
  total no.s = 3 + 8 + 5 + 2 + 7 + 6 = 31
  
• 10 years agoHelpfull: Yes(62) No(5)
• Ans: There are 31 nos between 2000 and 2199 which are perfect square,,
  Solutions:
  As 2194= 2 +1+9+4=16, Similarly 2002=2+0+0+2=4 (a perfect square),2007,2011,2016,2020,2025,2034,2043,2052,2059,2061,2068,2070,2077,2086,
  2095,2101,2106,2110,2115,2124,2133,2142,2149,2151,2158,2160,2167,2176,2185,
  2194.....total 31 numbers...
  
  
• 10 years agoHelpfull: Yes(17) No(8)
• sqare starting from 4 to 16 ie 4,9,16
  for 4 = 2 1 1 0,2 0 1 1,2 1 0 1, 2 0 2 0, 2 0 0 2, = total 5
  for 9= 2 1 1 5, 2 1 5 1, 2 1 6 0, 2 1 0 6, 2 1 2 4, 2 1 4 2,2 1 3 3,
  2 0 6 1, 2 0 1 6,2 0 4 3, 2 0 3 4,2 0 5 2,2 0 2 5,2 0 7 0,2 0 0 7 =15
  for 16= 2 1 9 4, 2 1 4 9= 2
  tatal 22 numbers possible
  
• 10 years agoHelpfull: Yes(0) No(19)
• @rakesh question is for 4digit number but u consider for 3digit
• 10 years agoHelpfull: Yes(0) No(2)
• ans is 22
  just try for the combinations with sum of no. as 2,3,4,5 because the greates no. possible is 2999 and hence greatest suare must be equal or less then 29
• 10 years agoHelpfull: Yes(0) No(3)