Alvin and Jethro Eric the Sheep There is a line of sheep waiting to be shorn. Eric is last in the line and too impatient to wait his turn, so every time the shearer takes a sheep from the head of the line, Eric jumps forward two sheep. Since you know how many sheep are in the line in front of Eric at the start, how many will be shorn before Eric gets to the head of the line?
Jethro and I used counters to experiment and collect the data in the table below. No of sheep in front (n)
Sheep shorn (s)
1
1
2
1
3
1
4
2
5
2
6
2
7
3
8
3
9
3
10
4
11
4
12
4
We noticed that when the number of sheep is a multiple of 3, then the number of sheep shorn will be changed. Therefore, we can work out a theory as below: If the number of sheep in front of Eric are multiples of 3, then the number of sheep shorn will be nรท3. n is the number of sheep in front of Eric.
If n is not a multiple of 3, we divide n by 3. Then the quotient plus 1 is the number of sheep shorn. Toolbox to prove our theory I used “Guess and Check� to prove our theory, and it worked. Extension If Eric jumps 3 sheep for each one that is shorn. We use the counters to collect the data and find the table below: No of sheep in front (n)
Sheep shorn (s)
4
1
5
2
6
2
7
2
8
2
9
3
10
3
11
3
12
3
13
4
14
4
15
4
16
4
17
5
18
5
19
5
20
5
21
6
We noticed that when the number of sheep is a multiple of 4, then the number of sheep shorn will be changed. Therefore, we can work out a theory as below: If the number of sheep in front of Eric are multiples of 4, then the number of sheep shorn will be nรท4. n is the number of sheep in front of Eric. If n is not a multiple of 4, we divide n by 4. Then the quotient plus 1 will be the number of sheep shorn.