RSM Addiction

Frank Kaszar may be the first person to be suffering from Road Sign Math addiction. For this post, his submission is being included verbatim.

Dear Administrator,

I am terribly pleased to finally be submitting this sign. I noticed it in February and was fascinated by the numbers involved. There were a lot of them, but they worked together surprisingly well. The numbers were 172, 172, 165, 165, 41, 43, and 57. I began working on the sign because 43 went evenly into 172 to make 4, which is a conveniently square number. However, as I continued to work with these numbers I was stunned at all the other interesting ways they worked together. Other square numbers besides that initial 4 can be found relatively easily. 43 + 57 is 100, and 57 - 41 is 16. If you use the 4 garnered from 172 / 43, you can do 165 + 4 to get 169 or do 172 + 4! to make 196. Furthermore, 172 - 165 is 7. If you add that to 57 you've got 64 and if you subtract it from 43 you get 36. These seven square numbers are only a few of the fun ways that these numbers work together.

Although there were so many ways to manipulate the numbers, I was chagrined to find that it wasn't particularly easy to find a solution. For several weeks most of the time that I had previously spent doodling in class was spent working with these numbers. I tried everything I could possibly think of. I was very often close (several times I noted that if I had a 1 the problem would have worked out) but I never came to a real solution. It was frustrating not finding a solution, but I couldn't give up on these numbers because I kept finding new ways to work with them.

This brings us to late March. I was out driving one day and I thought I would humor myself by driving past the sign to make sure that I had all of the numbers correct. As I came to the sign, I sighed because yes, I had all of the numbers right. However, just as I was passing the sign, I noticed out of the corner of my eye a sign apart from the other signs on the structure. I wasn't sure if I had seen it correctly so I had to get off at the next exit and come back to see it again. It seems that somehow, in trying to make a mental note of all of the numbers above the road, I had neglected the 45 mph on the ramp sign. I was thrilled! This number was the key to solving the mystery that had haunted me for more than a month. Now that I had 45, the solutions began rolling in. It's amazing how much of a difference one number can make.

I have included in my submission the picture of the sign (of course), but also a picture of several equations that use these numbers. After all that work and such diverse ways of manipulating these numbers, I couldn't let it go just submitting one solution. You don't have to post them all, I just wanted to share them because I was so fascinated with how these numbers work together. I had to write them because I didn't know how to type some of this stuff out. I hope you don't mind, and I hope it's legible. If not, let me know and I will try something else. The first equation on the sheet is the one I would like for my official one, as it has the highest overall score. The second one is the most elegant of the bunch (just addition and subtraction). The rest are all just sort of fun and use different functions.

Thank you for making your way through this verbose e-mail. Sorry for the length, but I thought the story was worth it. Have a fantastic day.

Sincerely, Frank Kaszar

Have a fantastic day indeed! Without further ado, Mr. Kaszar's sign.



Mr. Kaszar puts together a great string of square roots. Break it down yourself, it's a nice simplification, I think you will be impressed.

$$\sqrt{172-165+57} = \sqrt{45-41} + \sqrt{43-(172-165)}$$

Mr. Kaszar also includes his worksheet with the alternative solutions for this sign. Well done sir!



This sign is on highway 41 southbound near Green Bay, Wisconsin.