The citizens of planet nigiet are 5 fingered and have thus developed their decimal system in base 8. A certain street in nigiet contains 1000 (in base 5) buildings numbered 1 to 1000. How many 3s are used in numbering these buildings? Express result in terms of base 10.
a) 54 b) 64 c) 75 d) 100

• no of 3s b/w 1-99 is 20,100-199 is 20 and so on. so leavn d range b/w 300-399 total no of 3s is(9*20=)180. no of 3s b/w 300-399 is(20+100=)120.
  total no of 3s b/w 1-1000=120+180=300
  in base 10 300=3*5^2=75.
  ans:c
  
  
  
  
  
  
  
  
  
  
  
• 12 years agoHelpfull: Yes(20) No(17)
• Keeping the fact in mind that the decimal system of citizens is in base 8,
  we have,
  unit place no of 3's are given as....3,13,23,.....73
  103,113,123,.....173
  203,213,223,.....273
  303,313,333,.....373
  likewise upto 703,713,723,.......773
  hence total no of 3 in unit's place=8*8=64
  
  again, no of 3's in decimal place are as follows
  30,31,32,33.....37
  130,131,132,.....137
  .........
  730,731,732,......733
  i,e(8*8)=64
  
  Hence total no of three between 1 to 1000=(64+64+64)=192
  i,e (8*8)=64
  and total no of 3s in 100's place will be
  300,301.....307
  310,311,....317
  ...............
  370,371,....377
  
  
• 12 years agoHelpfull: Yes(12) No(11)