Readers Write: October 2001
I WOULD LIKE TO COMMENT ON THE “Four Fours” letter that appeared in the February 2001 issue (p. 340). I have assigned this problem several times in the course of teaching middle school students and have always been impressed with the results. One year, I challenged the students to generate the numbers between 0 and 100 using only four 4s and the basic operations, as well as factorials, square roots, and exponents. (I had not heard of the “next to” operation that was discussed in the letter but will allow its use in the future.) In the letter, Barry D. Cohen writes that he does not believe that 19 can be made using any of the regular or special operations and suggests that it requires the use of .4. I was not sure how to generate 19 with .4, but one of my eighth-grade students was able to generate it in this manner: 19 = 4! −(4 + 4/4). This student was unable to find solutions for a few other numbers between 0 and 100, including 35, 37, 43, and 51, and several in the 70s and 80s. I would love to hear if anyone has results for these numbers. Thank you for putting out such a fine publication.