This week the #puzzle is: Can You Spot the Sheep? #topic

Two sheep are at two random points inside a square pen. They are munching grass and staring in two random directions. Each sheep has a field of view that’s 180 degrees.

What is the probability that they both see each other?

And for extra credit:

Now, three sheep are at three random points inside a square pen. They are munching grass and staring in three random directions. As before, each sheep has a field of view that’s 180 degrees.

What is the probability that all three sheep see each other?

Can You Spot the Sheep?

Solution, possibly incorrect:

Program

Method 1:

• For sheep 1, there’s a 50/50 chance, that it’s facing the right direction to see sheep 2.
• Same for sheep 2 seeing sheep 1.
• Combined this is 25% or 0.25.

Method 2:

• Write a monte carlo program. Result confirmed.

And for extra credit:

Expand program to a 3 sheep situation. Result: 0.0272.