8 - 11 year olds

In a square whose side measures 5, there is a stair-shaped line joining two opposite vertices, as shown in the drawing.

​

The steps are all the same and the height is the same as the width.

​

We put a robot at one end of the ladder (vertex of the square. See drawing).

The exit of the square is at the opposite end of the stairs.

​

The robot always has to go forward, never back and it is programmed to perform an ODD number of steps each time it starts up.

​

Each step is a segment. The robot cannot skip segments and must step on both horizontal segments and vertical segments, once on each. In the drawing we see that the robot needs a total of 10 steps to exit.

a-- Can the robot come out with a single command?

Can the robot come out with two commands?

Can the robot come out with three commands?

Think why.

​

b-- If the square has 6 squares per side, would the answer be the same in each case?