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It is great that so many of you really enjoyed this problem, particularly the pupils of Canon Palmer Catholic School.

We have had an entertaining time reading your stories. Some of you made the problem more interesting by moving both the sheep and the man, and looking at relative distance.

Our favourites are shown below:

Graph One

The first one is anonymous:


2 weeks ago there was a mad shepherd, who lived on a farm in the middle of nowhere. His name was Dan.
There was another farmer down the road called James and every year they had a contest to see who had shaved off the most wool.
Dan was behind because his sheep kept running away, so he started to hi-jack James' sheep and take his wool.
But one day James made a plan to stop him taking his sheep: he put a long row of wet cement on the ground so that when Dan went across he would get stuck.
But when this happened not only Dan got stuck, but so did the sheep and they were stuck there for 2 hours.

In graph one, the distance between the man and the sheep is always the same. The story above describes the sheep and the man being stationary over time. Here is another story, this time from Sebastian of Canon Palmer Primary School, who tells a rather gory story...

There once was a farmer a very bad farmer who killed sheep. I know what you're thinking: "If you're a farmer then you have a right to kill sheep."
Well he didn't kill his own sheep, he stole the little cutie ones people keep as pets.
He was so bad that he went to prison for six years.
When he got back he got a court order so that he couldn't go closer than four metres near to a sheep.
That is why the man is always the same distance from the sheep.

When the man and the sheep keep the same distance between them, are they walking in straight lines, or could the man be walking in circles?

Graph Two

Well done to Neha who has made up a nice story to accompany graph two, which illustrates the man moving away from the sheep at a steady speed.

Farmer Ted is very good with sheep. One day he goes to feed the sheep but realises they are not there. He runs around the farm not realising that the sheep are hiding behind the shed.
He goes further and further away from the sheep.
It has been minutes and the farmer thinks that his sheep might have actually escaped the farm altogether. He runs out of the farm and he is still searching right this minute...

Graph Three

Thank you to Vipanjeet, who gives a scenario for graph three. Here a man walks away from a sheep at a steady speed, and then returns.

The man is walking to the river to feed his sheep.
When he is half-way there he remembers that he left the sheep behind. So when he gets back it is too dark to go to the river and feed the sheep.