Homework SourseImagine a number line with the integers marked Your old pal
Imagine a number line with the integers marked. Your old pal Grover starts at 0, and once per second takes a step to the left or a step to the right. (Being Grover, he probably sings a song about left and right as he does this.)
(a) Is it possible for Grover to take three steps and end up back at 0?
b) Suppose that Grover ends his meandering at k. What can you say about the number of steps n that he took?
c) How many ways are there for Grover to take four steps and end up back at 0?
(d) How many ways are there for Grover to take n steps and end up back at 0? (e) How many ways are there for Grover to take n steps and end up at k?
Imagine a number line with the integers marked. Your old pal Grover starts at 0, and once per second takes a step to the left or a step to the right. (Being Grover, he probably sings a song about left and right as he does this.)
(a) Is it possible for Grover to take three steps and end up back at 0?
b) Suppose that Grover ends his meandering at k. What can you say about the number of steps n that he took?
c) How many ways are there for Grover to take four steps and end up back at 0?
(d) How many ways are there for Grover to take n steps and end up back at 0? (e) How many ways are there for Grover to take n steps and end up at k?
(a) Is it possible for Grover to take three steps and end up back at 0?
b) Suppose that Grover ends his meandering at k. What can you say about the number of steps n that he took?
c) How many ways are there for Grover to take four steps and end up back at 0?
(d) How many ways are there for Grover to take n steps and end up back at 0? (e) How many ways are there for Grover to take n steps and end up at k?
Solution
Imagine a number line with the integers marked. Your old pal Grover starts at 0, and once per second takes a step to the left or a step to the right
Namely (0)(1)(0)(1)(0), (0)(1)(0)(-1)(0), (0)(1)(2)(1)(0), (0)(-1)(0)(1)(0),
(0)(-1)(0)(-1)(0), (0)(-1)(-2)(-1)(0),
