The citizens of planet nigiet are 8 fingered and have thus developed their decimal system in base 8. A certain street in nigiet contains 1000 (in base 8) buildings numbered 1 to 1000. How many 3s are used in numbering these buildings?
a) 256
b) 192
c) 54
d) 64

• Ans: 192
  
  Number 3 in 1-100 comes 20 times.
  101-200-> 20 times
  201-300-> 20 times
  301-400->120 times
  401-500-> 20 times
  501-600-> 20 times
  601-700-> 20 times
  701-800-> 20 times
  801-900-> 20 times
  901-1000-> 20 times
  Total times: 300 times (any no. from 1 to 9 except 0 will occur 300 times)
  8 based planet.. then
  3*8^2 + 0*8^1 + 0*8^0 = 192
• 11 years agoHelpfull: Yes(57) No(10)
• In base 8 System the digits are 0,1,2,3,4,5,6,7.
  The building numbers from 1 to 1000 in base 8.
  The number of 3s in one digit numbers is "1"
  The number of 3's in two digit numbers(30,31,32,33,34,35,36,37,13,23,43,53,63,73) is 15.
  The number of 3's in three digit numbers is (300......307,310....317,320.....327,330...337,340....347,350....357,360.....367,370......377 AND 103,203,.....703,113.......713.......AND 130....773.)60+56+56
  So total number is 1+15+56+56+60=192
  HINT::Use permutations Principle.........
  
• 13 years agoHelpfull: Yes(43) No(12)
• n*2*8+n^2
  works for everything below 10
• 13 years agoHelpfull: Yes(21) No(17)
• there are 300 3s in between 1 to 1000.
  converting (300)base 8 to decimal no. system we get
  =3*8^2
  =192
• 13 years agoHelpfull: Yes(13) No(3)
• the appropriate will be 3n^2.
  this works for everything below base 10
• 12 years agoHelpfull: Yes(8) No(2)
• 192
• 13 years agoHelpfull: Yes(7) No(3)
• I got 201 as answer.I cant see option here.Could any1 explain how 192 comes!
• 13 years agoHelpfull: Yes(6) No(11)
• 192
• 13 years agoHelpfull: Yes(3) No(0)
• 0 to 7 has 1 ‘3’, 00 to 77 ve 1*8+8 = 16 ‘3’s ..similarly 100 to 177 have 16 ‘3’s ….. 700 to 777 have 16 ‘3’s.. but 300 to 377 have 64 ‘3’s => total 8*16+64 = 192 ‘3’ s
• 13 years agoHelpfull: Yes(3) No(2)
• For these kind of question please follow the simple rule
  No. = 3n^2.
  this works for everything below base 10
  where n is the given base system in question
• 9 years agoHelpfull: Yes(3) No(1)
• 192
• 13 years agoHelpfull: Yes(1) No(3)
• Ans:200
  
  Number 3 in 1-100 comes 20 times.
  101-200-> 20 times
  201-300-> 21 times
  301-400->120 times
  401-500-> 20 times
  501-600-> 20 times
  601-700-> 20 times
  701-800-> 20 times
  801-900-> 20 times
  901-1000-> 20 times
  Total times: 301 times
  8 based planet.. then
  3*8^2 + 0*8^1 + 1*8^0 = 200
  Read more at http://www.m4maths.com/406-The-citizens-of-planet-nigiet-are-8-fingered-and-have-thus-developed-their-decimal-system-in-base-8-A-certain.html#jTUogQVj6Wv8gBmf.99
• 8 years agoHelpfull: Yes(1) No(0)
• plzz expalin simple logic 2 ans it..becoz its very lneghty.
  
• 11 years agoHelpfull: Yes(0) No(4)