TCS Company HR Interview Interview

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) 54 b) 64 c) 265 d) 192

Read Solution (Total 3)

in unit's place, the 3's are:
3, 13, 23 ... 73
103, 113, 123 ... 173
...
703, 713, .... 773
=> total number of 3's in unit's place is 8*8 = 64
in 10's place (that's 8 in decimal), the 3's are:
30, 31, 32... 37
130, 131, ... 137
...
730, 731, .... 737
=> total number of 3's in 10's place is 8*8 = 64
in 100's place (that's 64 in decimal), the 3's are:
300, 301, ... 307
310, 311 ... 317
...
370, 371 .... 377
=> total number of 3's in 100's place is 8*8 = 64
thus, the total number of 3's in total is 64 + 64 + 64 = 192
13 years agoHelpfull: Yes(54) No(2)

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
12 years agoHelpfull: Yes(35) No(0)
192

64+64+64 =192
13 years agoHelpfull: Yes(4) No(9)

TCS Other Question

Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line, .i.e the point lies on one side of the line while the others lie on the other side.
The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 5 points in the plane in general position(.i.e no three points in P lie on a line) is

a)3 b)5 c) 2 d)1 Given 3 lines in the plane such that the points of intersection form a triangle with sides of length 20, 20 and 30, the number of points equidistant from all the 3 lines is
a) 1 b) 3 c) 4 d) 0