math puzzle

[milagros317]

It has been a long time since I posted a math puzzle here, so here is a new one.

A mathematician attended a basketball game recently and, when it was over, she noticed something quite astonishing.

The visiting team and the home team each scored a prime number of points in each quarter and all eight of these primes were distinct (no two were equal). The score was tied after regulation time, after all four quarters had been played.

In overtime, the home team scored yet another different prime number of points (the ninth distinct prime), and the visiting team scored 0 points.

What is the lowest final score possible?

Yes, the lowest possible final score can be determined from just the information given above.

(Answer will be posted in one week, on September 10th, if nobody has solved it before then.)

 

[milagros317]

The solution is that the lowest possible final score is 54 to 52.
It can happen in any of 1152 ways:

The home team scores 3, 7, 13, and 29 points in the four quarters in any of 24 orders, for a total of 52 in regulation time.
The visiting team scores 5, 11, 17, and 19 points in the four quarters in any of 24 orders, for a total of 52 in regulation time.
That makes 24x24=576 ways of winding up in a 52-52 tie.

OR

The home team scores 5, 11, 17, and 19 points in the four quarters in any of 24 orders, for a total of 52 in regulation time.
The visiting team scores 3, 7, 13, and 29 points in the four quarters in any of 24 orders, for a total of 52 in regulation time.
That makes another 24x24=576 ways of winding up in a 52-52 tie.

After any of these 576+576 = 1152 ways of winding up in a 52-52 tie, the home team scores 2 points in overtime to 0 by the visiting team.