Latest TCS Aptitude Question SOLUTION: 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

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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

Solution

The general fundamental for finding answer will be following
from 0 t0 9, 3 will come 1*(1) = 1 times
from 00 to 99, 3 will come 2*(10) = 20 times
from 000 to 999, 3 will come 3*(100) = 300 times
similarly others
now the following question is based on any other system so take the following steps
from 0 t0 9, 3 will come 1*(1) = 1 times
from 00 to 99, 3 will come 2*(6) = 12 times
from 000 to 999, 3 will come 3*(36) = 108 times
from 0000 to 9999, 3 will come 4*(216) = 864 times


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Asked In TCS X22 (12 years ago)

Solved Read Solution (3)

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Read Solution (3) :

sourav  (12 years ago)

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

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Ankit Vora  (12 years ago)

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 :)

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Vikash Kumar Sharma  (12 years ago)

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

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