[ *July 16, 2001* ]

The palindrome story for 89

told by Terry Trotter (†) (email)

__Background__

I first learned about palindromes in general, and the two famous

problems about the reverse-and-add procedure with the numbers

89 and 196, sometime in the late 60's. Stanley Bezuszka, of Boston

College, had come to Kansas to give a session at a math teachers'

conference, and he presented the problems to us. He commented

that math teachers often couldn't do the 89 problem correctly

on their first attempt. They would frequently make silly, little

errors, then think they'd found the palindrome. As their errors

were pointed out to them, they began to realize that what, at first,

seems so easy, becomes hard if they aren't careful.

__The story__

My first year working here in the Escuela Americana of San Salvador

(1981) I used this problem one Friday with a group of 20-25 seventh

graders. Supposedly it was an elite group of kids, and for the most

part it was. So every Friday was a 'fun day', in which I dug into my bag

of recreational math topics and presented "Trotter Math" to them.

After explaining the reverse-and-add procedure on the chalkboard

with about 3 examples, I then said, "Ok, anybody want to make some

money ?" Now I had their full attention.

I continued, "I'll give one colon to the first person who can bring

to me a palindrome, correctly computed, beginning with the

number...(pause)...89 ! Begin now."

Pencils were beginning to move rapidly on all their papers. Soon

someone shouted, "I've got it !" and rushed up to me with his paper.

"Sorry," I said, "look, there's an error here. Go back and work some

more." Another soon did the same, but with a different error. Then

another, and so on.

I decided there needed to be a new rule, to get them to slow down

and be more careful. I said, "Ok, now. If you bring me something with

an error on it, you must pay me 25 centavos as a fine. But if you're

correct, I'll pay you the colon, of course. Is that a deal ?" They agreed.

But they continued to come forward... with incorrect work. I was getting

a nice collection of 25-centavo coins. Some even had to borrow a coin

from a friend in order to show me wrong work.

Finally, a girl, who had been quietly working all the while, raised

her hand, and said softly, "Mr. Trotter, I think I have it." Well, Claudia

was not a good student in math. Never was, in all the 3 years she was in

my classes. So I was sure she had made a mistake, too. But I said, "Bring

your paper, please."

So she did. I'm sure you can guess the rest --- it was exactly right !

All 24 addition steps leading to the 13-digit palindrome were there. And

she was the first student I ever had, and one of the very few, to do it

on the first attempt.

Oh, yes, the money. I awarded her all the coins the fast students had

paid to me in fines, over 2 colones, as I recall. Everybody had a good time

and learned a good math lesson. And the whole affair didn't cost me a

'centavo' of my own money !