DK-GEORGMOHR 2001

For the Georg Mohr game, a playing piece is used, a Georg Mohr cube (i.e. a die whose six sides show the letters G, E, O, R, M and H) as well as a game board: With each stroke, you advance to the next field with that letter the cube shows; if it is not possible to advance, one remains standing. Peter playing the georg mohr game. Determine the probability that he completes played in two strokes.

If there is a natural number $n$ such that the number $n!$ has exactly $11$ zeros at the end? (With $n!$ is denoted the number $1\cdot 2\cdot 3 \cdot ... (n - )1 \cdot n$ ).

In the square $ABCD$ of side length $2$ the point $M$ is the midpoint of $BC$ and $P$ a point on $DC$ . Determine the smallest value of $AP+PM$ .

Show that any number of the form $$4444 ...44 88...8$$ where there are twice as many $4$ s as $8$ s is a square number.

Is it possible to place within a square an equilateral triangle whose area is larger than $9/ 20$ of the area of the square?