Finding a Pattern: Eric the Sheep sneaks up 2 places in line

[jessica098]

"Eric the Sheep is at the end of a line of sheep waiting to be shorn. But being an impatient sort of a sheep, every time the shearer takes a sheep from the front to be shorn, Eric sneaks up the line two places."

I am asked to describe a rule or expression that I could use to find the number shorn before Eric for any number of sheep in front of him. I'm having trouble doing this.

I did some math, however, and created a table:

# of sheep in front of Eric / # of sheep shorn before Eric
4 / 2
5 / 2
6 / 2
7 / 3
8 / 3
9 / 3
10 / 4
11 / 4
12 / 4
13 / 5

Can anyone help me find the rule??

 

[mmm4444bot]

Re: Finding a Pattern



It looks to me like you may either describe the rule in words or write a formula. Describing the rule is easier to do than writing a mathematical formula.

Do you notice a pattern?

Hint: Let N represent the beginning number of sheep in front of Eric. Divide N by 3 for several consecutive values of N, and examine the quotient and remainder along side the values you posted in your chart.

Cheers,

~ Mark