Solutions

Puzzle 1

Two matches fit exactly as shown.

Each space has an area of 3 units. Look at the kite which is made up of two triangles each of area 1 ½ units.

Puzzle 2

Here is an explanation of the way the matches perfectly divide the space;

The triangle is a 3 4 5 triangle as shown here. A line of 1 unit (one match) is added 3 units along the base.

When a congruent right angle triangle DEF is constructed at the point F then

DF will be perpendicular to AC,

DF= 5 units

DE = 4 units

EF = 3 units

Continuing DE to A creates a third congruent right angled triangle ADG in which AD=5, DG=4, AG=3 units

It is now clear that GF = DF – DG = 5 – 4 = 1 unit

AG = 3 units and GC = 2 units as in our match stick triangle.

A similar construction allows us to see what happens in the 6,8,10 triangle when three matches are placed perpendicular to the base at the 7 cm point; the match of 1 unit length once again fits perfectly.

Solutions

Puzzle 3 Puzzle 4

Puzzle 5 Puzzle 6

Puzzle 7

2 equal parts

3 equal parts

5 equal parts

6 equal parts