In puzzle with n movable fields,
points are given according to how fast correct associations are found and how
many new associations are still possible:
- The first correct answer yields
n points, if it is achieved at the first attempt,
n - 1 points if it is achieved
at the second attempt, etc.
- The second correct answer yields
n - 1 points if it is achieved
at the first attempt,
n - 2 points if it is achieved
at the second attempt, etc. etc., until finally the number of points achievable
shrinks to zero.
The maximum number of points possible is
n
(n + 1)/2.
This is precisely the number of steps after which the puzzle may be resolved in any case.
On the interpretation of the number of points achieved:
Draging fields randomly until the correct position has been found, yields - on
the average - just half of the maximum number of points possible.
A positive result has thus been achieved if the number of points
is considerably above half the maximum.
In case your result is considerably less than half
the maximum, you display a systematic tendency to incorrect answers
(maybe on account of some misconception biasing your understanding of the subject
in a systematic way).