How to Play
Overall, gameplay is very similar to typical Scrabble; however, unlike typical Scrabble, you'll be using digits instead of letters (we'll cover your tile bag later). The objective is to achieve a higher score than your opponent while building prime numbers:
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself.
For clarity, a number is considered valid, only if it is prime.
Numbers are awarded a base score represented as the sum of their tiles. For example, take the number $127$, assuming that none of the digits occupy a multiplying tile, the base score for the number is $1 + 2 + 7 = 10$.
Additionally, per traditional Scrabble rules, if all 7 of a player's tiles are played in a single turn, an additional 50 points are awarded.
As with traditional Scrabble, there are multiplier tiles on the board that impact the base score:
- A double digit (DD) tile doubles the value of the digit occupying it.
- A double number (DN) tile doubles the entire base score of the number played.
- A triple digit (TD) tile triples the value of the digit occupying it.
- A triple number (TN) tile triples the entire base score of the number played.
If we calculate the total score for the number $127$, assuming the $2$ occupies one of these tiles per calculation, the scores would be $12$, $20$, $14$ and $30$ repsectfully.
Fibonnaci primes are special in that they are both Fibonacci numbers, and prime numbers. When one is played, the resulting total score is doubled. Take the number $131$ for example; assuming that it doesn't occupy any multiplier tiles, the total score is $1 + 3 + 1 = 5$ and the final score is $(1 + 3 + 1) \cdot 2 = 10$.
The Tile Bag
The tile bag is distributed based on Benford's law and contains 110 tiles:
$1$x30, $2$x17, $3$x13, $4$x10, $5$x8, $6$x7, $7$x6, $8$x5, $9$x4, $0$x8 and 2 blanks.
As with traditional Scrabble, the game ends when:
- There are no valid moves remaining.
- A player runs out of tiles.
- A player concedes.
Now, for the moment you've been waiting for! What is the highest achievable score in a single play? For your answer, you can assume that the board already contains a number that is advantageous to your goal with relation to your tile rack.