#DailyBloggingChallenge (142/200)
TIL that the #Jenga instructions differ depending on the language.
In English it says that after taking a block from the tower to place it on the top. Whereas in German it adds the additional information that it needs to be perpendicular to the blocks on the layer below it.
That additional info reduces the amount of choices from infinity down to a minimum of three as long as the distance from the center is not considered.
| Let the smallest area of sides be denoted front $F$ and back $B$ and the center line as $C$. Then typically the distance of $ | F - C | = | B - C | = b/2$ with $b$ as block length. Though, no where in the rules does it say that this equation has to hold up. Let $R := {<,=,>}$ be a relation, then $ | F - C | R | B - C | $ is still true with $ | F - C | \in [0, b]$. Since the distance $ | F - C | $ from the center is in a non one element interval, there are infinite solutions. (1) |
To get the minimum of three, one needs to count the amount of ways one can place a block, which is three: smallest area side, mid area side, and largest area side.
Additionally to this placement there is a rotation variable $r$ which has to be 90° or $\pi/2$. Otherwise without this restriction $r \in [0, \pi)$ and this would again give infinite solutions.
So going from the English instructions which would create infinite placement options down to German instructions, without (1), would give 3 placement possibilities.
Technically speaking, placing the blocks on the largest area side is a house rule.
