2017 Finals: Word Play

Description
This workbook is taken from the Second Round of the 2017 Modeloff financial modeling world chamionships.

Follow the instructions in order to complete the model:

The provided workbook includes the SOWPODS list of 267,752 English language words (the meaning of
SOWPODS is not important for the question, but it relates to a popular word-based board game).

Your task is to build a model that has the following functions:

When supplied with
i) An input string of 7 letters (e.g. F I N A N C E) or an input string of 6 letters and a wildcard;
ii) a value for N equal to 5, 6, 7 representing the length of the words; and
iii) a value for X (a positive integer)

Your model should be able to identify:
1) How many unique words of length N from the List can be made using the input letters. (For clarity, the
order of the letters can be rearranged, and each input letter can only be used once per word. So, if
FINANCE was the input string and N is 5, INANE (2 N’s) is allowed but FENCE (2 E’s) is not. Also,
count INANE once only, not twice.);
2) For a given value of X, the Xth word in an alphabetical sorted list of the words found in (1);
3) Which word from those found in (1) scores the highest amount of points when placed in its optimal
spot on the Board (details on next page). If more than one word scores the maximum, give the word
that would appear first in an alphabetical list of the highest scoring words; and
4) The score achieved from the optimal placement of the word in (3) above.

Each letter (A to Z) has been assigned a points value (from 1 to 10), and the wildcard will share the points
value of the letter it represents. The points per letter can be found on the ‘Scoring’ worksheet of the
provided workbook.

The Board is a 1 * 13 array of squares, with each square having a multiplier value of 1, 2 or 3. A word
may be placed on the Board with 1 letter per 1 square starting in any position on the Board, provided that:
i) The placement runs continuously from left to right;
ii) The middle square (#7) is always occupied;
iii) The whole word is placed and final letter does not extend past the end of the Board.

Allotted time: 60 + 20 minutes

Once finished, feel free to upload your model to your own dedicated author channel!