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# Matchstick boxes

Can you use 20 matchsticks (line segments of equal length) to form 5 squares?

Can you use 16 matchsticks to form 5 squares?

Can you use 6 matchsticks to form 5 squares? (Hint: Think out of the box)

Note by Chung Kevin
3 years, 5 months ago

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All three done.

SPOILER BELOW

20: Make five separate unit squares. 16: Make a chain of five unit squares connected side-to-side. 6: Make a unit square, then put the two matches to divide the square into four smaller squares. · 3 years, 5 months ago

Suggest: The problem also mentions each solution must not break matches, no matches must remain (all matches must be part of each solution),

A primitive square (needing the least matches) must contain four matches.

With 20 matches you must make five separate primitive squares (no shared matches).

With 16 matches you must share matches, and some squares must be primitives.Four separate primitives can be formed using 16 matches. Therefore four matches must be shared. Stick the four primitives together, two up (Row1) and two below (Row2), Each primitive shares a match/edge with its horizontal and vertical neighbor). The large composite formed (two matches per side for the outer square) is the fifth square. The internal 'plus' of four matches are all shared.

With 6 matches, you must first make the primitive (4 matches used up). The remaining 2 matches must somehow create four more squares. This obviously means the solution must lie inside the primitive (outside the primitive, an additional primitive square can only share one match, and needs three more). When it becomes obvious what needs to be done, you need to think logically, and 'within' the box! The two matches will form a plus sign within the primitive. This necessarily means the matches will overlap (something the problem does not expressly forbid).

I have created matchstick puzzles, some of which can be found here. Send feedback. http://www.problemsolvingpathway.com/pspsamples/PuzzledProblemSolving.pdf · 1 year, 7 months ago