Matchsticks – some classics

Here are 2 problems from Henry Dudeney:
1) New match problem^**

In the illustration eighteen matches are shown arranged so that they enclose two spaces, one just twice as large as the other. Can you rearrange them (1) so as to enclose two four-sided spaces, one exactly three times as large as the other, and (2) so as to enclose two five-sided spaces, one exactly three times as large as the other? All the eighteen matches must be fairly used in each case; the two spaces must be quite detached, and there must be no loose
ends or duplicated matches.

2) The six sheep-pens^**

Here is a new little puzzle with matches. It will be seen in the illustration that thirteen matches, representing a farmer’s hurdles, have been so placed that they enclose six sheep-pens all of the same size. Now, one of these hurdles was stolen, and the farmer wanted still to enclose six pens of equal size with the remaining twelve. How was he to do it? All the twelve matches must be fairly used, and there must be no duplicated matches or loose ends.

Both appeared in Dudeneys “Amusment in Mathematics”.

You can check your solution here and here

Matchsticks – the 3×3 square (1)

Remove 8 matchsticks so that you have
1) 5 squares left
(2 solutions, can you find them both?)
2) 4 squares left
3) 3 squares left
(2 solutions, can you find them both?)
4) 2 squares left

Safety matches, as we know them now, are not very old- they date from 1850–55. They have given rise to a vast array of puzzles – even my modest puzzle library has at least two books entirely developed to matchstick puzzles. Puzzles, like many other topics, are a product of the culture in a certain age. After matchsticks are replaced by other means of making fire, these puzzles will disappear.

If you are puzzled, you can look up the solution solution 1,
solution 2,
solution 3,
solution 4

You can find more puzzles of this type in one of our e-books

Matchsticks (1)

Move 2 matchsticks in each of the three number groups to get a correct equality:

If you are puzzled, we have a solution for you.

I would like to thank my collegue Harrie Jans for passing on this puzzle.

You can find more puzzles of this type on one of our e-books