Problem 1Edit

You tear a piece of paper in half 5 times. How many scraps of paper are you left with?

You should have 32, or $2^5,$ scraps of paper left over. The general solution is:

$P = 2^r$, where P is the number of paper scraps and r is the number of times the paper has been torn.

An interesting anecdote related to this problem: it was once commonly believed that a piece of paper could only ever be folded 8 times; thus, when unraveled, the paper could contain at most 256 ($2^8$) sections. However, this was later proven false when Britney Gallivan folded a paper 12 times, and derived a function for the actual number of folds that could occur.

Problem 2Edit

Problem from previous page

Problem 3Edit

Problem from previous page