In the game "Scribble", players place tiles containing individual letters on a board to form words. The board is divided up into squares, and each letter in a word is placed in adjacent squares in a row (reading from left to right) or a column (reading from the top down). Each letter has a point value, and the score for a word is found by adding up the point values for each of its letters. The point values for each letter are shown in the following table.
| Letter | Number of Points |
|---|---|
| A, E, I, L, N, O, R, S, T | \(1\) |
| D, G, U, Y | \(2\) |
| B, C, M, P, W | \(3\) |
| F, H | \(5\) |
| J, K, V | \(8\) |
| Q, X, Z | \(10\) |
For example, the word POUR would have a score of \(3+1+2+1=7\).
Players alternate turns making words on the board. After the first turn, each new word must build off of one of the letters already on the board. The score for any new word includes the point value for the letter that was already on the board.
Vinny and Theo played Scribble. Their game board is shown after they each had three turns.
Which word on the game board has the highest score?
Which word on the game board has the lowest score?
If Vinny made the first word, what is the maximum total score that he could have for his three words? In order to achieve this score, which word(s) could he have started with?
Extension: Suppose Vinny's next word has a score of \(10\). Which word could this be? See how many different possible words you can find. You can assume that the game board extends past the size of what is shown above.