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Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.



This second part is independent of the first one, but you can find the first part of this puzzle at the following link:

In recent years a very old game has become more and more famous: Mölkky. It is an authentic Finnish game that combines skill and luck. The goal is simple. Players must throw a wooden cylinder called Mölkky, in order to knock down the pin group (consisted of 12 pins numbered from 1 to 12) located 3 or 4 meters from the pitcher to score points and reach exactly 50 points.

Points are scored in this way:
- If a player knocks down only one pin, he scores the number of points marked on that pin.
- If a player knocks down more than one pin, he scores the number of pins knocked down (the numbers marked on the pins become irrelevant).

The purpose of this puzzle is to know how many possibilities there are to make 50 points from an initial score.

In this new edition, the only assumption made is that the player will hit at least one pin, but has as many rounds as necessary.


When P is placed in front of a number, it means that only one pin is knocked down and the number following the letter P is the number marked on the pin. On the contrary when the number is not accompanied it means the number of pins knocked down. The spaces separate the rounds. Before each round, all pins are put back in place.

If we start from a score of 47 then the possibilities are:
P1 P1 P1
P2 P1
P1 P2
2 P1
P1 2

There are 7 possibilities.
An integer N that matches the initial score.
An integer corresponding to the number of possibilities to reach 50 from the initial score
0 ≤ N ≤ 49

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