Another "Faulty Odometer" Problem #2

Number Theory Level 4

In this faulty odometer there is no digit 8.

After 7 it will show 9, after 79 it will show 90, etc.

What is the true reading if the faulty no 8's odometer reads 2197 ?


The answer is 1618.

Guiseppi Butel by Guiseppi Butel , 90, Canada

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2 solutions

Dinesh C
Jul 23, 2014

1618 is a answer....

2197-579=1618.

579 is total no of digit 8 from 1 to to 2197 ((19x9)+100)x2)+37)

2 Helpful 1 Interesting 1 Brilliant 1 Confused
Dheeraj Kumar
Aug 11, 2020

here decreasing the value of the digits >8 by 1 gives 2187. since there are 9 numbers only i.e {0,1,2,3,4,5,6,7,9}, we can consider the number is in the base 9 system. converting 2187 into base 10 gives (2×9^3)+(1×9^2)+(8×9)+(7×9^0) = 1618.

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