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

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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 ...show more

Best Answer

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)

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)

### Other Answers (2)

Rated Highest-
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. -
Nigiet, please. D's your answer.

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