Neurobics

Word Numbers

Russell Dear

In the Christmas issue, readers were challenged to find the highest "word number". A Word Number was defined to be a meaningful sentence in which the number of letters matched the numerical worth. For example, half a score has ten letters and a numerical value of ten.

A selection of specific high values were submitted, from 67 to 73,135, with readers showing great inventiveness. I particularly liked Dale Copeland's comment, after giving a solution for 67, that "ambition stirred" as he developed a method using repetition for 6337 (running to nearly three full typewritten pages).

Some readers realised that by making use of repetition there is no limit to the greatest Word Number that can be achieved. For example, half a score = 10, half a score and eight = 18, half a score and eight and eight = 26, and so on. Since "and eight" has eight letters, it can be used repeatedly to achieve a number greater than any you care to mention. Lloyd Esler suggested that the highest number attainable was four and six and six and , claiming the solution one centillion as the highest number recognised by the Guinness Book of Records.

Perhaps the most comprehensive entry was submitted by Colin Cheyne of Dunedin, who not only printed out ten pages for 73135 but gave formulae to generate various solutions of unlimited size. To Colin goes the prize copy of Kiwi Conundrums -- congratulations.

One wonders what numbers can't be written as Word Numbers. Bruce Hook and Stephen Horn began to write consecutive Word Numbers from ten. They began half a score, two plus nine, eight and four, twelve plus one, thirteen and one, sixteen minus one. Combining these repeatedly with "and six", any number above fifteen can be reached. For example, half a score and six = 16, two plus nine and six = 17, and so on.

So, are there any (whole) numbers that can't be reached? Perhaps some of those below ten. One, two and three could be difficult. 4 = FOUR. How about 5 to 9? See if you can find answers to those.

A Short Problem

Three farmers; Alan, Bob, and Craig and their sons Dan, Ernie, and Fred (not necessarily in the same order) each buy calves. Each buys as many calves as he gives dollars for one. Each father pays altogether $63 more than his son. Alan buys 23 calves more than Ernie. Craig buys 11 more than Dan. What is the name of each man's son?

Russell Dear is a Mathematician living in Invercargill