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

Nate thought a minute, then a smile came across his face. "Ohhh, now I get it. You just measure from the 3 mark to the 8 mark and that distance is 8 - 3 = 5 inches! Excellent! Does it work with all of the possible lengths?" Sally looked over the ruler for a little while and then answered, "Yes, I think it does. Let's make a table of all of the possibilities." Her table started like this:

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

Working together, Sally and Nate filled in the rest of the table, so that it looked like ... Can you fill in the rest of the table before you check on Sally and Nate's work? Click here to see what they did.