The citizen of a planet are 6 fingered and thus have developed a number system in base 6. a certain street in the planet contains 1000 buildings, numbered from 1 to 1000. how many 3's are used in numbering these buildings? express in base 10

• as the number system is in base 6 so in 0 to 10 counts the numbers can be from 0 to 5..in 100 the numbers can be 0-5,10-15,20-25,30-35,40-45,50-55....the topmost number can be 555 in 0-1000.
  the total no of 3's are(12+12+12+48+12+12)=108
• 12 years agoHelpfull: Yes(16) No(4)
• the answer is 724
  
  The numbering for first 6 houses will be 00,01,02,03,04,05. So for first six houses 3 occurs once. Similarly for next 12 houses. So for fist 18 houses we have used 3 3's. Now the next 6 houses will have numbering as 30,31,32,33,34,35. Therefore 7 3's. Again for next 12 houses 2 3's will occur. Therefore total number of 3's used in numbering 36 houses is 12
  
  36 houses--->12
  72 houses--->24
  108 houses--->36
  144 houses--->48+36( because numbering will be 300,301,302..so on)
  180 houses--->96
  216 houses--->108
  
  So 216 houses need 108 3's
  
  Again we follow the same process. But the crack here is that 1000th house will have a number of 4344. Keep that in mind to count the 3's.
  
  So 216 houses--->108
  432 houses--->216
  648 houses--->324
  864 houses--->432+216 (because the numbering will be 3000,3001,3002..so on)
  =648
  now next 36 houses--->12
  72 houses--->24
  108 houses--->36
  136 houses--->36 + 28 + 12
  total 3's=648 + 76
  =724 :)
• 12 years agoHelpfull: Yes(0) No(0)
• as numbering is from 1 to 1000 and sytem is in base 6 ;and our system is in base 10 so total number of buildings in our system will be ((60% of 1000) =600 ) and as after every 6 numbers there is one 3 and so in giving 600 numbers there will be 100 3's
• 12 years agoHelpfull: Yes(0) No(0)