Tasty teasers

Gruelling grids

1) What is the smallest number of straight lines you need to draw across a 3 x 3 grid so that every cell in the grid has at least one of the lines passing through it? The answer is less than three. Draw your solution.

2) What is the smallest number of straight lines you need to draw across a 4 x 4 grid so that every cell in the grid has at least one of the lines passing through it? The answer is less than four. Draw your solution.

3) Place five stones on the 8 x 8 grid shown below in such a way that every square consisting of nine cells has only one stone on it

The remaining questions all ask you to draw a pattern on a grid of 16 dots, shown below.

4) A polygon is a shape in which each side is a straight line. The H polygon below has 12 sides and the K has 13. Draw a polygon on the grid with 16 sides. (Note: each side of the polygon must join two dots. Lines cannot overlap. The shape, which need not resemble a letter, must have no gaps in its outline, and each dot can be passed through at most once.)

5) Below is a single square made by joining four dots in the grid. Find the other 19 squares that can be made by joining four dots. (Lines connecting the four dots may pass through other dots.)

6) The illustration below shows a way to connect 14 of the dots with lines, such that the angle at every dot is acute (i.e., less than 90 degrees). Find a way to connect all 16 dots so that there is an acute angle at every dot.