Match Tip Investigation – Notes

Investigation 1

It is not possible to make Match Top Puzzles with 1,2,3 or 5 matches. Apart from these cases it will always be possible to make a pattern.

An even number of matches can be placed in a loop, for example like four matches in a square. Two more matches can always be added into the loop.

And the same argument applies to odd numbers greater than 5. Another two can always be added in the same way.

Investigation 2

Here are some conditions you may have discovered about the numbers in the brackets.

a) The sum of the numbers in each bracket equals the number of matches

b) There is never a 1

c) The largest number in either bracket must not be greater than the the number of values in the other bracket eg (4,2) (2,2,2) cannot be possible. The 4 in the heads bracket means that there are 4 matches meeting at a point. Each will have its own tail, so there must be 4 values in the tails bracket)

Investigation 3

With 6 matches the possible listings are (2,2,2) (2,2,2) and (3,3) (2,2,2).

The first of these is simple. The second can only be built in 3 dimensions.

With 8 matches the possibilities are

(2,2,2,2) (2,2,2,2) (3,3,2)(2,2,2,2) (3,3,2) (3,3,2)*

(4,2,2) (2,2,2,2) (4,4) (2,2,2,2)*

Solutions in 3-D are shown by an asterisk*

With 10 matches the possibilities are

(2,2,2,2,2) (2,2,2,2,2) (3,3,2,2) (2,2,2,2,2)

(3,3,2,2) (3,3,2,2) (4,2,2,2) (2,2,2,2,2)

(4,2,2,2) (3,3,2,2) (4,2,2,2) (4,2,2,2)*

(4,3,3) (3,3,2,2)* (4,3,3) (2,2,2,2,2)*

(4,4,2) (2,2,2,2,2)* (4,4,2) (3,3,2,2)*

(5,3,2) (2,2,2,2,2)*