Hand-shakes and Fence-posts

1. Handshake Problem #1: Assume there are 20 people in a room, including you. You must shake hands with everyone else in the room. How many hands will you shake? If there are N (where N > 0) people in the room, how many hands will you shake? (Hint: Write a mathematical expression/equation)
2. Fence Post Problem: You need to build one side of a fence that is 12 yards long. This fence will be built with fence posts and rails that connect one fence post to another. If each fence post is 1 yard away from the next fence post, how many fence posts will be needed for this side of the fence How many fence posts will be needed for a side of a fence that is N (where N > 0) yards long?

3. Handshake Problem #2: Assume there are 10 people in a room, including you. Each person in the room must shake hands one time, and only time, with all the other people in the room. How many handshakes will occur? If there are 20 people in the room, how many handshakes will occur If there are N (where N > 0) people in the room, how many handshakes will occur?
4. Reflections: Why are problems like these important to learn how to solve? How could this type of solution be of benefit to a carpenter, a chef, a teacher? 

1. 
p=people

 h=handshakes

P

H

0	0
1	0
2	1
3	2
4	3
5	4
6	5
7	6
8	7
9	8
10	9
11	10
12	11
13	12
14	13
15	14
16	15
17	16
18	17
19	18

20

19

p-1=h

2. 
f=fenceposts
y=yards

F

Y

1	0
2	1
3	2
4	3
5	4
6	5
7	6
8	7
9	8
10	9
11	10
12	11
13	12

f-1=y

3.
p=people

h=handshakes

P

H

0	0
1	0
2	1
3	3
4	6
5	10
6	15
7	21
8	28
9	36
10	45

P(P-1)

2    =H