Matchsticks – some classics


Here are 2 problems from Henry Dudeney:
1) New match problem**
Dudeney matchsticks 204 exercise
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**
Dudeney matchsticks 205 exercise
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

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