October 13

Fibonacci numbers 

We write all possible sequences of black and white dots, such that no two black next to each other. How many different sequences are there?

2  of length 1 of them; 

3 of length 2; 

5 of length 3... 

Writing them one under another - if longer sequence extends the shorter one - helps.

Can you extend this picture? write all the sequences - without two black dots nearby! - of lengths 4... 5...

Robots still wandering 

how many ways to walk from the starting point to each of the crossings? Try to draw all the paths (or write them as instructions: North-West-North...

Find the number of paths to each crossing!

Eulerian graphs.

SET

Still the baby version: put the card that has three features the same as the one on the table.

Experiment 

rope on two pegs; one peg removed - rope slides off.