WordsWorth Times Composite Number Quest





Introduction
Bob Albrecht has authored a number of different educational games. For example, Hurkle or HurkleQuest, in many different variations, has been widely played for many years.

The WordsWorth game material given below is provided with the permission of Robert Albrecht via email to David Moursund on 4/13/08. There are many different versions of WordsWorth games.

WordsWorth Times Composite Number Quest
This particular WordsWorth game is is particularly interesting because it helps students engage in learning about and using both words and numbers.

Assign a letter score to each letter in the alphabet, a through z. The letter scores are the number 1 and the first 25 prime numbers:

a = 1   b = 2    c = 3    d = 5    e = 7    f = 11    g = 13    h = 17    i = 19    j = 23

k = 29 l = 31   m = 37  n = 41  o = 43  p = 47   q = 53    r = 59     s = 61   t = 67

u = 71 v = 73   w = 79  x = 83  y = 89  z = 97 Uppercase letters (A, B, C, …, Z) have the same letter scores as their lowercase counterparts.

The WordsWorth Times (WWT) of a word is the product of the letter scores of the word's letters. Thus, for example:


 * WWT of aha  is 1 x 17 x 1 = 17


 * aha is a palindrome.


 * 17 is a prime number.


 * 17 is an emirp.


 * WWT of dad  is  5 x 1 x 5 = 25


 * dad is a palindrome.


 * 25 is a composite number.


 * 25 is a square number.


 * WWT of big is 2 x 19 x 13 = 494


 * 494 is a composite number.


 * 494 is a palindrome.

The domain of WordsWorth Times is an agreed-upon set of words. We use words defined in the dictionaries listed here:


 * The Official Scrabble Players Dictionary, Third Edition (or later edition). Copyright (c) 1996. ISBN: 08141300699. You can buy it online used for about $6 plus shipping.


 * Internet: Dictionary.com (http://dictionary.reference.com/)

OR, instead of a designated dictionary, use a word list of your choice. The object of Composite Number Quest is to find words that have a WordsWorth Times equal to a composite number. We suggest: 1. For each composite number less than 100, find a word whose WWT is equal to that number. 2. Find words that have WWTs equal to special numbers such as
 * Square numbers: 1, 4, 9, 16, 25, ...
 * Triangular numbers: 1, 3, 6, 10, ...
 * Fibonacci numbers: 1, 2, 3, 5, 8, ...
 * Et cetera, et cetera.

Reality expands to fill the available fantasies… The Hurkle Hiders [Bob & George]