Pay attention to the time bar!

Probability Level 3

During a soccer match there is a time bar that shows the time in minute and seconds.It is of the form $ab:cd$ where $ab$ shows the minutes for example $05$ and $cd$ shows the seconds for example $45$ .Thus the time would be $05:45$ .The soccer match lasts $90$ minutes and it is divided into two halfs each of $45$ minutes.

How many times does it happen during the match that the time bar is of the form: $ab:ba$ for some positive integers $a$ and $b$ including $0$ ?

Note:
Assume there wasn't any extra time at the end of each half.
The match lasts from $00:00$ to $90:00$ .

The answer is 54.

1 solution

Tristan Shin
Aug 19, 2014

First, choose $a$ . $a$ must be from $0-8$ , as $9$ would be over the time limit. Next, choose $b$ . This must be from $0-5$ , as anything $6$ or over would not be eligible in the seconds part. By the Fundamental Principle of Counting, the total number of ways is $9 \times 6 = \boxed {54}$ .

Hey I think the Problem description is misleading, It mentions that the match is divided in two halfs therefore it could be understood that after the first half the clock is reset to 00:00 for the sencond half (as is done in many places for real matches). Then you have a different answer.

Jacob Salazar Solano - 6 years, 3 months ago

Thanks. I've updated the problem phrasing to indicate that.

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Calvin Lin Staff - 6 years, 3 months ago

Pay attention to the time bar!

The answer is 54.

1 solution

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