Habits of Mind Problem #2
The Sneaky Sheep
Due Sept 6, 2011
Eric the sheep is at the end of a line of 50 sheep all 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.
i) Under these conditions, what will be Eric’s “number” when he is shorn? Explain why your
answer is correct.
ii) Eric gets more (and more) impatient! Explore how the answer will change if Eric sneaks past 3
at a time or 4 at a time.
iii) Suppose there were (m) sheep ahead of Eric (m = 49 in the first part of this problem) and Eric
sneaks past (n) at a time, (m is greater than n), what number will Eric be when he is shorn?
Explain.
Statement of Authorship
My (our) signature(s) below indicates that:
1) I (we) did not use any resources such as the web or books other than our textbook.
2) I (we) did not get any help from any individual other than my peers in the class and my instructor.
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3) Below, I (we) have identified any other classmates with whom we discussed this problem whether they
gave us help or we gave them help.
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Individual Responsibility When Group Work is Permitted
Opportunities for group work include both situations when several people sign their name to the same
assignment and when one individual receives help from a classmate even when they do not submit assignments
together. Group work is permitted for Habits of Mind problems, projects, group presentations, etc. This is done
in the belief that, done right, it supports learning, minimizes stress when a mistake is made, and results in a
culture of achievement. Many of us recognize that it is often easier to work on something that is challenging if
we get to share the challenge (and the success) with peers. At the same time, the learning process can be
undermined when one person tells another the solution to a problem (instead of offering a helpful suggestion) or
when someone signs their name to an assignment when they did not contribute their fair share of effort.