A Farewell to 1987

An in-depth look back on a challenging Advanced Placement Math assignment

On the final school day of December 1987, my 10th Grade Advanced Math teacher, Mr. Mike Teachman, gave everybody in the class an extra credit assignment. The challenge: Write each number from 1 to 50 using the digits in 1987. He gave us the whole winter vacation to complete the assignment and our papers were due on January 4, 1988.

In order for the class to better understand this challenge, Mr. Teachman gave a sample problem: Write the number 100 using four 4's. At first, everybody was stumped, until he showed us the answer:

44/.44

As indicated in that example, decimal points could be used. Symbols (like +, -, and the square root sign) could also be used. But you could only use each digit in 1987 once, and you could not use any other number.

There were a few more rules for this assignment:

1. Each paper would be scored as follows: For each correct answer, 1 point would be added to your score; for each incorrect answer, 2 points would be deducted. If no answer was given for a problem, no points would be added or deducted.
2. Whoever had the highest score for the assignment would have 30 extra credit points added to their total grade. Those 30 points would be enough to raise the overall grade for the semester by about 2 points (so, for example, if someone was getting a B+, a perfect score on this assignment could have raised that grade to an A-).
3. Everybody would be competing against each other, which meant nobody would share answers.

As I got started on the assignment, I found that some numbers were easy to crack (like 2, 13, 16, 23 and 25; for more details, a scan of my paper appears below, and you can click on the image to get a full-sized copy).

(Click on the image above to enlarge it.)

As you can see on my paper, there was a simpler answer for #4 that didn't occur to me; I could have been written it as 91-87.

But a few other numbers seemed impossible, no matter how hard I tried. To borrow a phrase from WWE announcer Jim Ross, #24 was about as tough as a $2 steak.

Then one night, I realized that I needed to find more symbols to use--parentheses, brackets, decimal points and square root signs could only take me so far. I thought to myself, There was this symbol Mr. Ford mentioned when I was at Warner Middle School... what was it? (At that time, William M. Ford taught 7th and 8th grade Advanced Math at Warner.) After racking my brain for what seemed like a couple of hours, it came to me: The factorial, which is indicated by an exclamation point. (The factorial of a non-negative integer n is the product of all positive integers less than or equal to n. For example: 3! = 3*2*1 = 6.)

At first, it didn't seem like that exclamation point would do me any good, as the factorials of 7, 8 and 9 all yielded numbers much larger than 50, and the factorial of 1 is 1. But the square root of 9 is 3, and the factorial of 3 is 6, meaning I could, in essence, use a 6 without breaking the rules of the assignment. Long story short, the factorial helped me with a few hard numbers, like 22, 24, 35, 38, and 39.

(√9)! = 6

The real fun, though, didn't come until we returned from winter vacation. After we turned in our papers, Erica Watnick came up to me and asked me if I did all 50 problems, which I did, and she said she did, too. But she mentioned that she squared and even cubed some of the numbers to get her answers.

I figured that she had used 2 for squares and 3 for cubes; for example, she might have said...

35 = (7-1)² - 9 + 8

I was sure Mr. Teachman wouldn't allow that. But I didn't want to let her know that, so I acted astonished and said that it never occurred to me to do that.

As Mr. Teachman checked everyone's papers, Erica asked him how she fared:

EW: Do I have the highest score?
MT: Well, Rabo's already got you beat by 51 points.
EW: What do I have?
MT: Minus one.
EW: Is that what I have wrong?
MT: No, that's your score!

My paper had correct answers for all 50 problems. Erica, however, had 33 right and 17 wrong. Since 2 points were deducted for each incorrect answer, her paper had a score of -1. I was right after all: Squaring and cubing were not allowed.


Erica turned to me in shock and said, "Rabo, it's not fair!"

As it turned out, mine was the only paper to have 50 correct answers.

It also turned out that neither of us really needed the extra credit points--we both got A's. Still, for poor Erica, "A Farewell to 1987" might as well have been called "Goodbye--and Good Riddance--to 1987."

One more number-related thing to note about 1987: Prior to 2013, 1987 was the last year that all four digits were different--every year in between had one digit used twice.