One of my favorite topics to teach in Number Theory is the solving of coded messages. By using information on how often each letter appears in the English language, one is often able to figure out the relationship between seemingly random letters and meaningful words. This often begins by noticing how often letters appear in a code, and then relating those letters to the alphabet by noting which letters appear most often in English. For example, the letters E, M and S and T appear often in English, while Q and Z do not appear very often. Using this information, it is possible to deduce a formula relating each letter of a plain text message to each letter of a cipher. I found myself thinking of this recently as I traveled the country with my family in a car, playing the proverbial “letter game.”
There are actually two versions of the letter game, and we played both of them at some point on several road trips we have taken so far this summer. One version asks us to find the actual letters of the alphabet in order, letters that are found on signs or buildings or the side of trucks and cars. To make things a little more difficult, our family has chosen not to include letters on license plates, although names of cars written on the sides of cars are admissible. The other version asks us to find things that begin with each letter in order, and can actually be more difficult than finding the actual letter written out somewhere. As an example, it is almost impossible to find things that begin with the letter Z that might be found while traveling on a highway.
I know that the years of being able to play games with my daughter will soon be limited, and therefore I want to savor these fleeting moments of interacting with her as we travel to places near and far. Therefore, whenever she chooses to put down her electronic games or video player and asks to play the letter game with us, I always choose to jump at the opportunity. I suspect that in a few years she may not even want to go on vacation with us anymore, and that I have a short amount of time to build fond memories of time spent with her.
Although she knows nothing of Number Theory, I found myself thinking of the process of decoding a cipher as we searched for letters that appear very rarely in English. For example, the letter “J” and the letter “Q” were particularly difficult to find, as was the letter “Z.” Were it not for “Flying J” rest stops or signs advertising New Jersey, we probably would never have made it to the letter K in our travels. Z was actually easy to find in states that had E-Z pass programs, but Q was very difficult to find, especially if there was no Quality Inn for miles. Indeed, as we traveled to a graduation party in Pittsburgh recently, we found ourselves stumped by the letter Q. That was, until we drove through the city and noticed the college where the father of the graduate serves as a dean; Duquesne University.
I am wondering, as the summer progresses and we anticipate a few more short road trips, what other games my readers might play to pass the time in their travels. Do you have ideas for other games that can be enjoyed by parents and pre-teens alike?
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