We had lots of solutions sent in for this activity. Brookfield Junior School obviously got very involved and sent in many solutions. Here is an example of two of them.
Firstly, from Bill:

The formula to Ip dip is n≥8 when n stands for the number of friends so that means if the number of friends is eight or over you should be in the eighth position. To solve the first bit the position is the remainder of the number of the friends divided by eight. so the formula is p=8/n= the remainder.

Secondly from Tomas:

If you had two people  you would start in second position.
If you had three people you would start in second position.
If you had four people you would start in fourth position.
If you had five people you would start in third position.
If you had six people you would start in second position.
If you had seven people you would start in first position.
If you had eight people you would start in second position and so on.

From Mossley Primary School we had solutions sent in from Kati-leigh, Luke, Chiara,  Amelia and Emily. Here is one example:

2: start with friend
3: right friend clockwise
4: second to right clockwise
5: third to right clockwise
6: left clockwise
7: yourself
8: right clockwise
9: second to right clockwise
10: third to right clockwise
11: third to left
Thanks for reading.

Amelia and Bea from Barton C E V A Primary School sent in the following

If there were 8 or more players, then always go for the 8th place.
If there were fewer than 8 players then you would find how many players there are and see what number adds to the amount of players to get to 8.You may need to use multiplication facts with this:

7 players: 1x7= 7     7 + 1 = 8     You go in 1st place

6 players: 1x6= 6     6 + 2 = 8     You go in 2nd place

5 players: 1x5= 5     5 + 3 = 8     You go in 3rd place

4 players: 1x4= 4     4 + 4 = 8     You go in 4th place

3 players: 2x3= 6     6 + 2 = 8     You go in 2nd place

2 players: 3x2 = 6     6 +2 = 8     You go in 2nd place

This is because there are 8 words in the rhyme.

Thank you, all of you, for the ideas you sent in, in order to solve this challenge.