A car has a defected odometer(distance measuring device),it goes directly from 3 to 5,that it does not have the digit 4.As for example, when the odometer shows 39 and then travel one more kilometer,it should show 40 but instead , it shows 50. Now on a certain case the reading in odometer was 2005,determine the exact distance traveled by the car.
source- faridpur divisional math olympiad, 12th bdmo
faulty odometer
Re: faulty odometer
The answer is $1462$.
$\because$ The odometer doesn't have the digit $4$,count the number of the numbers which have at least one $4$ in it from $1$ to $2005$.There are $543$ numbers from $1$ to $2005$ which have at least one $4$ in it the car skipped them.So,the exact distance traveled by the car was $2005-543=1462$
$\because$ The odometer doesn't have the digit $4$,count the number of the numbers which have at least one $4$ in it from $1$ to $2005$.There are $543$ numbers from $1$ to $2005$ which have at least one $4$ in it the car skipped them.So,the exact distance traveled by the car was $2005-543=1462$
"Questions we can't answer are far better than answers we can't question"
Re: faulty odometer
I have got another approach which is easier
Assume that the number $2005$ is in base $9$.Now,convert it to decimal.
$2005(_{9})=2\times 9^{3}+0\times 9^{2}+0\times 9^{1}+5\times 9^{0}=1463$ .But,the number $2004$ is not counted.So,the exact distance traveled by the car is $1462$
Assume that the number $2005$ is in base $9$.Now,convert it to decimal.
$2005(_{9})=2\times 9^{3}+0\times 9^{2}+0\times 9^{1}+5\times 9^{0}=1463$ .But,the number $2004$ is not counted.So,the exact distance traveled by the car is $1462$
"Questions we can't answer are far better than answers we can't question"