Puzzles from the Math Midway
The Missing-Mark 12-inch Ruler:

Here's what Sally came up with: Put marks at 1 inches, 3 inches, 7 inches, and 11 inches. Then:

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
7-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
3-inch mark
11-inch mark
9 inches
3-inch mark
right end of ruler
10 inches
1-inch mark
11-inch mark
11 inches
left end of ruler
11-inch mark
12 inches
left end of ruler
right end of ruler

There are lots of fun problems like this. For a big challenge, try to find the fewest number of marks you can put on a yardstick to be able to measure any length from 1 to 36 inches.

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