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 when you
achieve considerably more than half the maximum number of points.
In case your result is considerably less than half
of the maximum number, you display a systematic tendency to incorrect answers
(maybe on account of some misconception biasing your understanding of the subject
in a systematic way).