Week #4 Winter 2015
of the Week
Solution
In the game of scrabble, players attempt to spell out words with letter tiles in an
attempt to get a large number of points. Points are scored using the value of
each of the lettered tiles (For example: The letter A is valued at 1 point, and the
letter Q is valued at 10 points). The word MATH would have a value of 9 points
since an M is valued at 3 points, A at 1 point, T at 1 point and H at 4 points (see
the tile distribution and point values below). It was said that Sam the Speller
once scored 50 points on a 7-letter word (using the values of the tiles alone).
What is the probability that if you select 7 random tiles, you will be able to spell a
50 point word?

2 blank tiles (scoring 0 points)

1 point: E ×12, A ×9, I ×9, O ×8, N ×6, R ×6, T ×6, L ×4, S ×4, U ×4

2 points: D ×4, G ×3

3 points: B ×2, C ×2, M ×2, P ×2

4 points: F ×2, H ×2, V ×2, W ×2, Y ×2

5 points: K ×1

8 points: J ×1, X ×1

10 points: Q ×1, Z ×1
Solution: From above it can be seen that the largest number of points that can
be achieved using 7 tiles is actually 49 points (the letters would include Q, Z, J, X,
K, and 2-four pointers). It is therefore impossible to get 50 points, so the
probability is 0%.