InterMath | Workshop Support | Write Up Template

Title
Alpha Numeric

Problem Statement
Fill in the next letter of the alphabet, using the logic established to list the first eight:

O, T, T, F, F, S, S, E, ____

(Source: Mathematics Teaching in the Middle School, Nov-Dec 1997).

Problem setup
Using the sequence of letters as they are arranged, figure out what letter comes next.

Plans to Solve/Investigate the Problem
I plan to use the existing numbers to see if there is a pattern or sequence or how they relate to each other in various ways (ex.  Distance from each other when the alphabet is written out, letter repetitions).

Investigation/Exploration of the Problem
My first thought was that the answer might be the letter “E” because there was a series of repeated letters and one “E” was already in place.  I was then told that the answer was not “E”.  Then I tried to see how many letters apart each letter was from the others to look for patterns such as the same number of letters between letters or a sequential increase in numbers (ex.  The first letter could be three spaces from the second and then there could be six letter spaces between the second and the third, indicating a doubling of the non visible letters if you replaced them with number values according to the alphabet sequence.)  Other additive and multiplicative patterns were considered.  We had been told to think “outside the box” and to take the title into great consideration.  It was frustrating to finally look at the numbers, 1, 2, 3, and so on, and see that each number correlates with the letter given in the number by using the first letter of each number (ex. 1 =one, 2 = two, 3 = three, 4 = four, etc.)

Extensions of the Problem
The process could go on forever and it’s hard to say whether or not it would be easier to determine the answer with a longer list of letters.

Author & Contact

Kevin Smith
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Link(s) to resources, references, lesson plans, and/or other materials