Memories: The Oral Story Problem Game

Homeschool Memories…

Perhaps you’ve heard me mention the oral story problem game. It was one of my favorite ways to get my children thinking about math, back in our early days of homeschooling. We played in the car on the way to soccer practice, or while we washed dishes, or sitting in the lobby waiting for a doctor’s appointment.

The rules are simple: I’ll make up a math problem for you to solve. And then you make up one for me.

The kids always loved trying to stump me.

This problem from Henry Ernest Dudeney’s Amusements in Mathematics reminded me of those days. This is exactly the way my eldest loved to torture me…

Dudeney Writes…

A certain cyclopaedia has the following curious problem, I am told: “Place fifteen sheep in four pens so that there shall be the same number of sheep in each pen.”

No answer whatever is vouchsafed, so I thought I would investigate the matter. I saw that in dealing with apples or bricks the thing would appear to be quite impossible, since four times any number must be an even number, while fifteen is an odd number.

I thought, therefore, that there must be some quality peculiar to the sheep that was not generally known.

So I decided to interview some farmers on the subject.

The first one pointed out that if we put one pen inside another, like the rings of a target, and placed all sheep in the smallest pen, it would be all right.

But I objected to this, because you admittedly place all the sheep in one pen, not in four pens.

The second man said that if I placed four sheep in each of three pens and three sheep in the last pen (that is fifteen sheep in all), and one of the ewes in the last pen had a lamb during the night, there would be the same number in each pen in the morning.

This also failed to satisfy me.

The third farmer said, “I’ve got four hurdle pens down in one of my fields, and a small flock of wethers, so if you will just step down with me, I will show you how it is done.”

The illustration depicts my friend as he is about to demonstrate the matter to me.

His lucid explanation was evidently that which was in the mind of the writer of the article in the cyclopaedia. What was it?

Can you place those fifteen sheep?

The Answer Is…

By the way, “The Answer Is…” is another of my favorite ways to play with math. You pick any number for the answer. Then everyone makes up problems to fit.

Often, we would use that day’s date as our problem-prompt. So, for example: “Today is January the-square-root-of-eight-squared.”

Anyway, did you figure out the sheep puzzle?

The key is in the image, and in the careful way Dudeney worded his story. If you have a child like mine, you know to look for a trick. But are you crafty enough to figure it out?

(I had to peek, but then my kids usually managed to stump me, too! If you give up, the answer is in the italic end-of-post notes below.)

Oh, and if you’d like to play a fun, cooperative sheep-counting game, check out Yan Tan Tethera, part of my Tabletop Math Games Collection.

How Is This Math?

Part of thinking like a mathematician is to examine our assumptions, to wonder how things might be different from what we expect.

• What if parallel lines really do meet at the horizon? How would that change geometry?

• What if infinity is even stranger than we thought? What if there is another infinity, even greater than the infinity of the counting numbers? Could there be an infinite number of infinities?

In mathematics, precision is not primarily about measuring accurately and keeping track of your decimal places. Precision means saying what you mean and meaning what you say. Being careful about definitions and wary of assumptions.

Because those unexamined assumptions will make you the perfect comedic “straight man,” always falling victim to your children’s jokes.