frogs

I didn't think or dream about school for the last five years. Then the last few nights I dreamed of waiting for the bus. I dreamed of going into classrooms I did not remember. The subject was always maths.

The roads in my dreams wound and the corridors were full of people I did not know. It sprawled like a hospital, a factory or a farm. I was in the wrong class room constantly and without my homework always. Anonymous authority figures. I dreamed of snapping and telling them fuck you. the indignation of an adult.

There was this maths problem that I could never figure out. The problem was set for us a few times in primary and secondary school:

There are lily pads in a line. You start with two frogs, one at each end of the line with the middle pad empty. The frogs can hop one pad at a time and can hop over one another when they are next to each other. The objective is to figure out the minimum number of moves required for the frogs to swap places.

Once you've done that, you do the same thing with two frogs at either end, again with one empty pad in the middle.

Then you do it again with three frogs either side...

 

You're supposed to take these numbers and use them to figure out an equation to express the minimum number of moves required to swap the places of any number of frogs in the same setup (i.e. equal numbers on either side with one empty pad in the middle).

 

I don't know why I needed to figure this out now. I could never do it in school and it made me feel bad about myself. I didn't have the guts to ask for help with it and I guess I had accepted it was the limit of what my brain could do. The problem was I panicked and didn't have the patience to examine the problem. When I came back to it and made an effort to move forward cautiously, a correct pattern gradually emerged. 

One time, when I was little, I saw a frog in the pond across the road from our house. I was wading in the water and disturbed it. The sky was the colour of the road and it rained and I stayed out in the pond until it was dark, waiting for the frog. When I finally gave up, I went inside and drew pictures of frogs instead.