Activity 30: Problems and Puzzles



This is a picture of the front double gates.

If you look at these gates each has a series of little knobs on the top like the drawing below:



You can see that there are five little knobs between the two end posts of the gate and that the distances between the knobs are all the same.

The gap in each case is 40 centimetres.

How far is it from the first to the second knob?

How far is it from the first to the fourth knob?

How far is it from the second to the fifth knob?

Draw a table showing these results and how you got them.

From this, is there a rule for finding how many gaps between points in a line?
When you have found the rule do the following.

If the gate followed the same pattern but had 20 knobs 10cm apart, how far from the fifth to the seventeenth knob?

Extra:

If you have a fence with 25 posts, 1 metre apart from their centres, and three