Puzzle: The Eccentric Teacher

One of my favorite things as a teacher was to gather a group of children to play math together.

Call it a math club or math circle, the name didn’t matter, but the activity was always fun. We did non-schooly games and projects, and the kids enjoyed both the camaraderie and the experience of thinking hard in a stress-free setting.

If you’d like to pull together a math club/circle of your own, here are some tips.

Today’s puzzle involves an unusual teacher trying to collect students to participate in a group activity…

The Original Story

It appears that an ingenious or eccentric teacher, as the case may be, desirous of bringing together a number of older pupils into a class he was forming, offered to give a prize each day to the side of boys or girls whose combined ages would prove to be the greatest.

Well, on the first day there was only one boy and one girl in attendance, and, as the boy’s age was just twice that of the girl’s, the first day’s prize went to the boy.

The next day the girl brought her sister to school. It was found that their combined ages were just twice that of the boy, so the two girls divided by prize.

When school opened the next day, however, the boy had recruited one of his brothers. It was found that the combined ages of the two boys were exactly twice as much as the ages of the two girls, so the boys carried off the honors that day and divided the prize between them.

The battle waxed warm now between the Jones and Brown families, and on the fourth day the two girls appeared accompanied by their elder sister; so it was then the combined ages of the three girls against the two boys. The girls won, of course, once more bringing their ages up to just twice that of the boys.

The struggle went on until the class was filled up, but our problem does not need to go further than this point. Tell me the age of that first boy, provided that the last young lady joined the class on her twenty-first birthday.

[By Sam Loyd, quoted by Martin Gardner in Mathematical Puzzles of Sam Loyd.]

Math for Young Children

It makes me wonder what the teacher intended to do with his students when he first gathered them.

Perhaps he had in mind some of the activities from the Early Family Math website, or Maria Droujkova’s and Yelena McManaman’s book Moebius Noodles?