## How many Cars at a Carpark?

Question

576 digits are used to record the number of cars at a car park. How many cars are there altogether?

Solution

It means as you record the number of cars using 1, 2, 3,.. 10, 11,… 100, 101 etc., a total of 576 digits are used to write all those counting numbers ðŸ”¢.

To find how many cars are there, we first find until which number must one write so that 576 digits are used exactly.

Count as follows:

1 to 9: A total of 9 digits are used to write these numbers

10 to 99:

A total of (99 – 10 + 1) x 2 = 180 digits are used to write these numbers.

100 to 199:

A total of (199 – 100 + 1) x 3 = 300 digits are used to write these numbers only.

So, far 9 + 180 + 300 = 489 digits are used to write the numbers from 1 to 199 in the above.

We require another 576 – 489 = 87 digits more.

Since 87/3 = 29, a total of 29 more 3-digit numbers are required beginning with 200.

Indeed, consider the writing of numbers:

200 to 228:

A total of (228 – 200 + 1) x 3 = 87 digits are used.

Thus, we have used a total of

489 + 87 = 576 digits to write all the counting numbers from 1 to 228.

Hence, there are

228 cars (Answer)

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