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# Three matches

## Question

If we place four matches in the form of a square, they form 4 right angles.

If we place them like a hash-tag (#) they form 16 right angles.

If someone removes one match, can we still form 12 right angles?
(No bending or breaking of the matches is allowed.)

## Recommended Posts

• 1

No

new improved snswer

Yes. Form two matches into an X on a piece of paper. Place the third match vertically through the paper adjacent to the intersection of the first two matches. Now , 4 right angles at each intersection of a pair of matches. There are three pairs of matches. 12 right angles.

Bonanova, you keep on educating me, I greatly appreciate it.

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Spoiler

An unwritten assumption is that a match is a representation of a line segment -- and another match placed perpendicular to it intersects that line segment as if it is on the same plane.  Independently understood but crediting Captain Ed for posting his first, Captain Ed's "new improved answer" implies that a third match is placed on a plane that may be perpendicular to the first plane. Given his extension to the unwritten assumption, indeed, it is possible to have12 right angles formed in the construction.

Given that the matches are not actually representation of line segments, but are often rectangular 3-dimensional boxlike shaped objects with right angles being formed along the edges, then there are an infinite number of right angles that are formed. Infinite is a non-numeric quantity that is inclusive of all smaller positive quantities which encompasses that of 12. Thus, within this scheme of the riddle one can can even form 12 right angles with but two matches. Thus the answer to the question posed remains YES.

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understand that even in the hashtag ,the matches were / are not in the actual same plane , then the following will result in 12 right angles.    Two of the matches are crossed giving us 4 right angles.  The 3rd match is vertical to the plane of the other two ,and extends equidistant  above and below the plane of the other two matches. The  vertical portion above the plane makes 4 right angles with the two crossed matches.  The vertical portion below the plane makes 4 more right angles   Total 12

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