how many numbers are there from 100 to 1000 in which sum of any two digit equal to the third digit..?

• sum of any 2digits equal to 3rd
  such 3digit no. with 0 in it are
  101(101,110),202,303,404,505,606,707,808,909(2 ways each)
  similarly
  112,224,336,448(3ways each)
  remaining
  123 235 347 459
  134 246 358
  145 257 369
  156 268
  167 279
  178
  189
  each can be written in 6 ways
  
  so total nos are 9*2+4*3+16*6=18+12+96=126
• 11 years agoHelpfull: Yes(58) No(0)
• in series of 100->101,112,123,134,145,156,167,178,189
  no =9
  in series of 200->202,213,224,235,246,257,268,279
  n0=8
  similarly for other
  so
  9+8+7+6+5+4+3+2+1=45
• 11 years agoHelpfull: Yes(7) No(22)
• so total numbers will be 9*2+4*3+16*6= 18+12+96=126
• 11 years agoHelpfull: Yes(3) No(2)
• @ Vani,
  
  Pls check cases when three numbers are different and no zero (0) is used..
  
  U hv considered
  Quote
  for different digits(with out 0): 1 can be sum up with 7 numbers ,2 with 6......8 with 1 ,9 with 0 number ...total:7*7+1/2=28 numbers(like 2+1,3+2.....different numbers )
  these can be written in 28*3! ways=168 ways
  
  unquote.
  
  I think u r considering same number multiple times.
  
  like 189
  when taking 3! of numbers with 189, u hv considered 189,198,891,819,918,981
  and same numbers u hv considered with numbers having 8.
  in case of 257 , u have considered same set of numbers 3 times in case of 2,5 and 7 and again taking 3! for each case.
• 11 years agoHelpfull: Yes(2) No(3)
• 116 Nos.
  
  Here sum of any two digit equal to the third digit.
  number like 101,110,112,121,211 ..... 945,954 are to be considered.
• 11 years agoHelpfull: Yes(1) No(2)
• same numbers like:1+1=2 ,2+2,3+3,4+4 each number can be written in 3!/2! =3 ways
  
  4 numbers 4*3=12----(1)
  
  for different digits(with out 0): 1 can be sum up with 7 numbers ,2 with 6......8 with 1 ,9 with 0 number ...total:7*7+1/2=28 numbers(like 2+1,3+2.....different numbers )
  these can be written in 28*3! ways=168 ways-----(2)
  
  with 0:1+0,2+0..... 9 numbers with each number in 2 ways
  
  9*2=18 ways---(3)
  
  total :168+18+12=198 numbers
  
  
  
  
  
• 11 years agoHelpfull: Yes(1) No(3)
• @ all my ans 66 is correct because i have attempted 6 question in in quants in my elitmus xam and all were correct so there should be no confusion
• 11 years agoHelpfull: Yes(1) No(13)
• @ Ankit,
  
  Pls clarify what do u mean by ..
  2,3,5.... 4ways ...I think 6 ways 235,253,352,325,523,532
  3,3,6 2ways .... 3 ways are possible...336,363,633
  4,5,9 2ways ...... 6 ways .. 459,495,549,594,945,954
  ..
  and some other similar cases ?
  
• 11 years agoHelpfull: Yes(1) No(1)
• 10
  one in each row of 10 no.(for e.g. 101 from 100 to 110 and so on )
• 11 years agoHelpfull: Yes(0) No(3)
• 1,0,1 2ways
  1,1,2 3ways
  1,2,3
  6ways
  1,3,4
  
  6ways
  1,4,5 4ways
  1,5,6 2ways
  1,6,7 2ways
  1,7,8 2ways
  1,8,9 2ways
  2,02 2ways
  2,2,4 3ways
  2,3,5 4ways
  2,4,6 4ways
  2,5,7 2ways
  2,6,8 2ways
  2,7,9 2ways
  303 2ways
  3,3,6 2ways
  3,4,7 4ways
  3,5,8 2ways
  3,6,9 2ways
  4,0,4 2ways
  4,4,8 2ways
  4,5,9 2ways
  total 66 such numbers
• 11 years agoHelpfull: Yes(0) No(17)
• ans...1665
• 9 years agoHelpfull: Yes(0) No(2)