Problem A

Scrabble Words

Scrabble^{TM} is a game where 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 a playerâ€™s score for placing a
word on the board is the sum of the point values for the letters in the
word. The point values for each letter are in the following table.

Letter | A | B | C | D | E | F | G | H | I | J | K | L | M |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Value | \(1\) | \(3\) | \(3\) | \(2\) | \(1\) | \(4\) | \(2\) | \(4\) | \(1\) | \(8\) | \(5\) | \(1\) | \(3\) |

Letter | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Value | \(1\) | \(1\) | \(3\) | \(10\) | \(1\) | \(1\) | \(1\) | \(1\) | \(4\) | \(4\) | \(8\) | \(4\) | \(10\) |

In the Scrabble board shown, the coloured squares have special values.

Blue squares, marked **B** on the board, are double
letter squares, which means if you put a tile on that square, then the
letter is worth twice as many points.

Grey squares, marked **G** on the board, are triple
letter squares, which means if you put a tile on that square, then the
letter is worth three times as many points.

Red squares, marked **R** on the board, are double word
squares, which means if you put a tile on that square, then the whole
word is worth twice as many points.

Orange squares, marked **O** on the board, are triple
word squares, which means if you put a tile on that square, then the
whole word is worth three times as many points.

Double and triple letter scores are calculated before the double and triple word scores.

How many points would the word EXACT be worth if you put the first letter in the first row and second column, and place the word horizontally across the board?

How many points would the word DEBUT be worth if you put the first letter in the second row and second column, and place the word vertically on the board?

How many points would the word CHEF be worth if you put the first letter of the word in the last column and third row, and place the word vertically on the board?

**Themes: **Geometry & Measurement, Number Sense