HOW MANY 3 DIGITS NUMBERS ARE THERE WHOSE SUM IS 18?

• Fix 1st digit as 1, then remaining two digits can be [9, 8] and [8, 9] ---- total 2
  Fix 1st digit as 2, then remaining two digits can be [9,7], [8,8], [7,9] and --- total 3
  Fix 1st digit as 3, the remaining two digits can be [9,6], [8,7], [7,8], [6,9]--- total 4
  Fix 1st digit as 4, the remaining two digits can be [9,5], [8,6], [7,7], [5,9], [6,8] --- total 5
  
  and so on... till 1st digit is fixed as 9 whose total is 10
  So adding all we get:
  2 + 3 + 4+ .....+ 10 =[ (10*11)/2 ] -1 = 55 -1 = 54
  
• 9 years agoHelpfull: Yes(14) No(0)
• I think its 54
  
  990 - 2 combinations
  981-6 combinations
  972-6 combinations
  963-6 combinations
  954-6 combinations
  882-3 combinations
  873-6 combinations
  864-6 combinations
  855 -3 combinations
  774- 3 combinations
  765 -6 combinations
  666-1 combination
• 9 years agoHelpfull: Yes(7) No(0)
• sum is 18 implies no.divisible by 9, so find no. of 3 digit no. ivisible b 9. ans-89
• 9 years agoHelpfull: Yes(1) No(3)
• 1+8+9=3! comination
  in this way 2+7+9
  2+8+8
  3+6+9
  3+7+8
  4+5+9
  4+6+8
  4+7+7
  5+5+8
  5+6+7
  total 60 comnination number and 6+6+6 it has only 1 combination .
  60+1=61 (ans)
• 9 years agoHelpfull: Yes(1) No(2)
• Fix last digit maximum and then 1 to 5 as a first digit, fill the middle number
  1 9--->8==189(ways)--->3!
  2 9--->7(ways)--->3!
  3 9--->6(ways)--->3!
  4 9--->5(ways)--->3!
  5 9--->4 (ways)--->3!
  2nd set (no starting with 1 will be eliminated since 1 cannot be summed to become 18 with other no)
  1 8--->NOT POSSIBLE
  2 8--->8(ways)--->3!
  3 8--->7(ways)--->3!
  4 8--->6(ways)--->3!
  5 8--->5 (ways)--->3!
  KEEP an eye on the previous results while writing the results of combinations
  3rd set
  4 7-->7(ways)--->3!
  5 7--->6 (ways)--->3!
  4TH set
  From here on number will be repetitive
  66 is the ANSWER
• 9 years agoHelpfull: Yes(1) No(0)
• 1+8+9=3! comination
  in this way 2+7+9=6 comb.
  2+8+8= 3 comb.
  3+6+9= 6
  3+7+8 = 6
  4+5+9=6
  4+6+8=6
  4+7+7= 3 comb
  5+5+8= 3 comb
  5+6+7= 6
  6+6+6 = 1 combination
  TOTAL = 52 COMBINATIONS.
  60+1=61 (ans)
• 9 years agoHelpfull: Yes(0) No(0)
• 990/18=55
  55-1=54....
• 9 years agoHelpfull: Yes(0) No(1)