UKMT Special (Problem 44)

My 2424-hour digital clock displays hours and minutes only.

How many displayed times in a 2424-hour period contain at least one occurrence of the digit



[UKMT JMO 20192019 Section B, B55]

Note by Yajat Shamji
7 months ago

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You have until this Friday, 3:003:00pm!

Yajat Shamji - 7 months ago

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Well, that's fifteen of 5 occurrences in an hour. We have 24 of these hours, but for the 5th and 15th hours, 5 will be present 60 times, for each minute. Thus,

Number of occurrences of the number 55 : 22×15+2×6022 \times 15 + 2 \times 60

(22 remaining hours have an occurrence of 5, fifteen times, and the other two hours have it the whole hour or 60 times)

The answer is : 450\boxed{450}

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@Yajat Shamji - Why is there a time limit for these probs? Just curious, is it coz' you'll be posting a solution after the given time? Anyway, is my answer correct?

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Yes, it's because I'll be posting the official solution...

As for answers, I can check...

Yajat Shamji - 7 months ago

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Your answer is correct!

But.. the method is different.

Yajat Shamji - 7 months ago

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@Yajat Shamji I see...okay then, I'll wait for your method...

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@A Former Brilliant Member You have to wait 3 days!


Yajat Shamji - 7 months ago

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