Question 1 Problem 1 (2.5 points).
Show that the Pulverizer algorithm produces gcd(a, b) =s xa +txb.
Hint: strong induction,

there is only one way to arrange all the eight relative to each other because they are not distinct. we have

now there are nine places to place an (and not more than one in one place).   because we have four symbols, we need to choose four of these nine places to insert an . order does not matter because the are not distinct.

thus there are 1 · c(9,4) ways, or, if we calculate it,

thus there are 126 ways to form such "words."

if you get paid hourly because if you get a salary you could work all week and only get paid a certain amount no matter how much you work but if you get paid hourly then you get paid for every minute you worked.