Sneaking Up the Line
Eric, the sheep, is at the end of the long line of sheep waiting to be shorn. But, being an impatient sort of
sheep, Eric sneaks up the line two places every time the shearer takes a sheep from the front to be
shorn. So, for example, while the first sheep is being shorn, Eric moves ahead so that there are two
sheep behind him in line. If at some point, it is possible for Eric to move only one place, he does that
instead of moving ahead two places.
1. Suppose Eric is the last in a line of 10 sheep. How many sheep would be shorn before Eric?
2. What is Eric is the last in a line that was 15 or 50 sheep long? How many sheep would be shorn
before Eric?
3. Describe how you could work out the answer for any number of sheep in a line?
4. Eric gets more and more impatient! Explore how your rule changes if Eric sneaks past 3 sheep at
a time, 4 sheep at a time, or even 10 sheep at a time. As soon as someone tells you how many
sheep are in front of Eric and how many he sneaks past a time, describe how you could work out
the answer.
5. Now the shearer is getting impatient! She hires some additional shearers. Explore how your rule
changes if the number of sheep taken to be shorn before Eric jumps changes. That is, describe
how you could work out the answer for any number of sheep in front of Eric, any number of
sheep he sneaks past at a time, and any number of sheep are taken at a time to be shorn.