Know your alphabet

Use each of the letters A, B, C, D and E.

Write one letter in every circle.

Letters joined by lines must not be next to each other in the alphabet.

Now try this one.

Perimeters

This shape has a perimeter of 12 units.

Add more squares to the shape so that they touch edge to edge.

What is the minimum number of squares that must be added to make a perimeter of 18?

What is the maximum number of squares that can be added to make a perimeter of 18?

SOLUTIONS

Know your alphabet (age 5 to 8) other solutions are possible.

Answers

Perimeters (age 10 to 14) Adding one square to a shape made from squares touching edge to edge could change its perimeter by +2, 0, - 2 or - 4 units, depending on where the extra square is positioned and the arrangement of squares in the original shape. At least 3 squares must be added to make a perimeter of 18. For example: the maximum number of squares that can be added to make a perimeter of 18 is 14, positioned so that the whole shape forms a 4 by 5 rectangle.