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  • How many Cars at a Carpark?

    Anonymous Christian
    Nov 7, 2016
    Math Olympiad
    Comments Off on 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 🔢.

    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)

anonymous-christian

Jonathan Ramachandran is founder at AnonymousChristian.org which serves as a Christian Blog discussing the Greater Hope of Biblical Christian in Christ Alone. He is also an IMO (International Math Coach) and a featuring Guitarist for many bands.

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