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Questions tagged [proof-without-words]

A puzzle asking about a proof (usually mathematical) expressed with diagrams and without words.

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5 votes
1 answer
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What does this prove?

Unfortunately, this image is too big for me to provide a transcription. Hint: Additional hint: Last hint: Hint: Hint: Since the hint is given, a viable solution must explain how it works.
Sny's user avatar
  • 3,165
9 votes
2 answers
228 views

A constant gaze

What this infinite spiral seems to be gazing at goes without saying. Yet, to go on and on heedlessly as if trying to prove something, let’s just say it represents an equality with a well-known ...
humn's user avatar
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20 votes
4 answers
4k views

Four buttons on a table

I was asked lately (in an interview) to solve this puzzle, which is similar to the 4 cups on table puzzle. In a certain room there is a rotating round table, with 4 symmetrically located ...
Jay's user avatar
  • 335
7 votes
1 answer
214 views

Proof by induction without words

This seems more like a proof about induction than a proof by induction.   But what is this proof really about? That is, what circuit with an inductance of 4 henries between A and B does that ...
humn's user avatar
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9 votes
2 answers
488 views

A big logical mess

I found a drawing under a stack of books in my house. It looked like a logical circuit diagram, so I decided to make it. I assumed that I was allowed to put anything in the boxes with the question ...
boboquack's user avatar
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7 votes
1 answer
662 views

There oughta be a law without words

There really oughta be a law. There really is! $\require{begingroup}\begingroup \small\sf \def \& { & \kern-.5em = \kern-.5em & } \def \l #1 / #2 { \log \frac {\normalsize #1} {...
humn's user avatar
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5 votes
1 answer
212 views

A strange traffic light

I saw a mysterious picture on an electronic whiteboard in a school I was walking past. I couldn't hear what the teacher was saying, but I could see on the timetable that it said 'Maths'. Can you work ...
boboquack's user avatar
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7 votes
1 answer
188 views

Proof without curves

  Say, what’s that in the distance?   Could be a road full of cars or a wire full of electricity, or whatnot, but this much is for sure:    It is straight and infinitely ...
humn's user avatar
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11 votes
4 answers
1k views

A line in Connect Four

When I was young, I was playing with a friend. Of course, the topic soon turned to mathematics (as it always does), and we got into an argument over something. We went on for some time, then he got ...
boboquack's user avatar
  • 22k
12 votes
2 answers
876 views

What the L are they trying to prove?

Seems some L t rominoes have developed a punk attitude and feel they have something to prove because people always play with dominoes instead.   They are even jealous of I trominoes, who ...
humn's user avatar
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6 votes
1 answer
384 views

Some day in the park with Fiqo

   “Awwwwhat a cute little diagram,” the stranger said, “what’s its name?”    “Fi qo.   (A ...
humn's user avatar
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26 votes
12 answers
4k views

Tiling a Hexagon with Diamonds

A regular hexagon is divided into a triangular grid, and completely tiled with diamonds (two triangles glued together). Diamonds can be placed in one of three orientations. Prove that, no matter how ...
Mike Earnest's user avatar
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