There is a 13 cm ruler. How many lines do you need to carve on it so that the ruler can measure all the whole centimeter's length from 1 to 13 cm at a time? Where to carve it?

We need to carve at least four lines, for example, at 1, 4, 5, 11 cm, then we can measure all the whole centimeter lengths from 1 to 13 cm at one time. This is because we can get 13 integers from 1, 4, 5, 11, 13 and the difference between them. See the following expressions: 5-4 = 1, 13-11 = 2, 4-1 = 3, 11-5 = 6, 11-4 = 7, 13-5 = 8, 13-4 = 9, 11-1 = 10, 13-1 = 12 It is proved that only three scales are not enough. If only three lines are engraved at a cm, B cm and C cm (0 < a < B < C < 13), then a. The difference between B, C and 13 (greatly reduced) is only 6 different numbers at most: 13-A, 13-b, 13-c, C-A, C-B, b-a. plus a, B, C, 13, there are 10 different numbers at most. It is impossible to get 13 different integers from 1 to 13

So you can just carve the length of all the four centimetres on the top of the ruler?

1,2,4,8

Some straightedge zero mark at the end, some not at the end, what are the advantages

The end is usually measured by the side against the raised edge, which is convenient
Not in the general kind, not afraid of angle wear

There is a 13 cm ruler. How many lines do you need to carve on it so that the ruler can measure all the whole centimeter's length from 1 to 13 cm at a time? Where to carve it?