Q2. The citizens of planet nigiet are 8 fingered and have thus developed their decimal system in base 8.?

Question

Q2. 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

Answer 1

Best Answer - Chosen by Voters

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
(d)

Answer 2

d) 192 is the correct answer.
These are the buildings with numbers containing 3:
3, 13, 23, 33, 43, 53, 63, 73, 30, 31, 32, 34, 35, 36, 37 (3 comes 16 times in total)
103, 113, 123, 133, 143, 153, 163, 173, 130, 131, 132, 134, 135, 136, 137 (3 comes 16 times in total)
203, 213, 223, 233, 243, 253, 263, 273, 230, 231, 232, 234, 235, 236, 237 (3 comes 16 times in total)
300-307, 310-317, 320-327, 330-337, 340-347, 350-357, 360-367, 370-377 (3 comes 9 + 9 + 9 + 17 + 9 + 9 + 9 + 9 = 80 times in total)
403, 413, 423, 433, 443, 453, 463, 473, 430, 431, 432, 434, 435, 436, 437 (3 comes 16 times in total)
503, 513, 523, 533, 543, 553, 563, 573, 530, 531, 532, 534, 535, 536, 537 (3 comes 16 times in total)
603, 613, 623, 633, 643, 653, 663, 673, 630, 631, 632, 634, 635, 636, 637 (3 comes 16 times in total)
703, 713, 723, 733, 743, 753, 763, 773, 730, 731, 732, 734, 735, 736, 737 (3 comes 16 times in total)
Therefore, 16 + 16 + 16 + 80 + 16 + 16 + 16 + 16 = 192.

EDIT: The solution by The Grannyator is more methodical and better than mine. Please vote that one the best answer.

Source(s):

Myself.

Answer 3

Nigiet, please. D's your answer.