3. On a wooden ruler, three marks are made: 0, 7, and 11 centimeters. How can you measure a segment of (a) 8 cm; (b) 5 cm using it?
$\Delta$ Using divisions by 7 and 11, it is easy to measure 4 centimeters. Doing this twice, we get a segment of 8 centimeters. Measuring 5 centimeters is a bit more complicated: knowing how to measure 8 and 7, we can measure 1 centimeter. Doing this 5 times, we get 5 centimeters. $\triangleleft$

We can do it differently: we know how to measure 4 cm and 1 cm, so we can measure them in sequence to get 5 cm. Another way: $5=3 \cdot 11-4 \cdot 7$, so it is enough to measure 3 times by 11 cm and then 4 times by 7 in the opposite direction. (The advantage of the method given first is that it works for any integer number of centimeters.)