Question

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 buildings numbered 1 to 1000 in base 8. How many 4's are used in numbering these buildings? Express your answer in base10.

Answer 1

Answer:

Step-by-step explanation:

In base 8 system 1000 can be written as:

divide 1000 by 8 and write remainders

1. $\frac{1000}{8} = 125$  remainder=0
2. $\frac{125}{8}=15$ remainder=5
3. $\frac{15}{8}=1$ remainder=7
4. $\frac{1}{8}=0$ remainder=1

so $1000_{10} =1750_{8}$

whenever 4 was there on 100th place 64 numbers are associated with it for 4 at 100th place and 4 will be on 100th place two times (400-477) & (1400-1477)

so total 4 on 100th position = $2\times 64=128$

now when 4 is on 10th place 8 numbers are associated with it. so total number of fours on 10th place = $8\times 2\times  8=128$

when 4 is on unit place, similarly number of 4 used= $174_{8}=124_{10}$

so 124 number of 4 will be at unit place.

so total number of 4 = 128+128+124=380