Puzzles from the Math Midway
The Ruler That Missed The Mark

One afternoon as Nate and Sally were walking home from school, Nate blurted out, sounding annoyed, "Maybe their printers were running out of ink!"

"What are you talking about?" asked Sally.

"The people at the Math Midway. Otherwise I can't figure out why the ruler they gave me doesn't work," explained Nate.

"What do you mean, `doesn't work?'"

"You see, when I was at the Math Midway exhibition the other day, I got a ruler that was printed out by the Organ Function Grinder. That was pretty cool -- the Grinder played a tune while it calculated a function I made up, and every time someone changed the function, it played a different tune."

"But what about the ruler?"

"Right. Like I said, at the end it gave me a ruler, which looked pretty excellent, so I stuck it in my notebook. And today, the teacher gave us some paper and told us to draw a five-inch square on it. `Great!' I thought, `I'll get to use my Math Midway ruler.' So I took it out, all excited, but whaddaya know? It didn't have any mark for 5 inches. So I had no way to draw my square. I had to borrow a ruler from John, and you know how mean he is... So the only thing I can figure out is they were running out of ink..."

"Let me see the ruler," Sally demanded. So Nate got out his ruler, and here's what Sally saw:

After looking it over for a little while, Sally continued: "Well, I don't know if they were out of ink, but it does seem as though they were saving on it. 5 is not the only missing mark on this ruler. But it's kind of interesting -- I can see how you could measure out a 5-inch square."

"Really? How?"

"Do you want a hint first?"


"Just remember, you don't always need to start measuring from one end of the ruler."

Nate thought a minute, then a smile came across his face. "Ohhh, now I get it. You just ..."

Now can you see how to measure five inches with this ruler? Try to figure it out before you click here to continue the story...