Fence posts and gaps

Hello, and welcome to Myriora Maths! A path is one hundred metres long. You plant a tree every five metres, from one end to the other. How many trees? If you said twenty, you've fallen into one of the most common traps in the 11 plus!

Let's try something smaller. A path ten metres long, with a tree every five metres. A tree at the start, at five metres, and at ten metres. That's three trees, but only two gaps.

So, the number of gaps is the length divided by the spacing. And the number of trees is the gaps, plus one. For our hundred metre path: twenty gaps, so twenty-one trees!

But what if the path goes round in a circle, like a fence around a pond? The last gap joins back to the first tree. So the trees equal the gaps. A circular path of one hundred metres: twenty trees.

And if there's a wall at both ends, with no trees on the ends? Then it's the gaps, minus one. Nineteen trees.

The same idea hides in other puzzles. Cutting a log into five pieces takes four cuts. And walking up from floor one to floor six takes five flights of stairs.

So, the common mistake is dividing, and stopping there. Always draw a small version first, and count.

Your turn! A fence is forty-two metres long, with a post every three metres, and a post at both ends. How many posts? You've got twenty seconds, or pause the video if you need more time. Go!

Time's up! Fourteen gaps, so fifteen posts!

Quick review. A straight line with both ends: the gaps plus one. A circle: the same as the gaps. No posts on the ends: the gaps minus one. See you next time!