Puzzles from the Math Midway
The Ruler That Missed The Mark Concluded

Working together, Sally and Nate filled in the rest of the table, so that it looked like.

To measure Measure from: and measure to:
1 inch left end of ruler 1-inch mark
2 inches 1-inch mark 3-inch mark
3 inches left end of ruler 3-inch mark
4 inches 3-inch mark 7-inch mark
5 inches 3-inch mark right end of ruler
6 inches 1-inch mark 7-inch mark
7 inches left end of ruler 7-inch mark
8 inches left end of ruler right end of ruler

When they were done, Nate was feeling much better. "I can't wait until the teacher asks us to measure a six-inch triangle -- I'll be ready and waiting with my Math Midway ruler!" And Sally was excited, too: "I wonder if you could do the same thing with an ordinary 12-inch ruler?"

What do you think? What's the fewest number of marks you could put on a 12-inch ruler and still be able to measure every distance from 1 inch to 12 inches? Try to solve it, and make a table of how to measure each one of the distances. When you're done, click here to compare your solution to Sally's.