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Transit Across a Purple Sun

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This very attractive geometrical puzzle is from Catriona Agg. It looks like there isn't enough information, although there is. See the Comments for my solution.

But even after solving it it still feels as though there is an information deficit somewhere!

Permalink 2 comments (latest comment by Jan Pinfield, Thursday, 4 Mar 2021, 15:07)
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A Geometric Puzzle

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Edited by Richard Walker, Sunday, 11 Oct 2020, 00:36

Here's an easy to understand geometric question, with a purely look-and-see solution. It comes from YouTuber Michael Penn but I have modified it slightly.

To be in the spirit of the traditional wooden Japanese temple offerings, called Sangahu, I have added decorative colours.


If the larger square is 1 x 1 and so has area 1, what is the area of the smaller square?

Permalink 4 comments (latest comment by Hazel Shaw, Wednesday, 14 Oct 2020, 23:47)
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Samurai Puzzle - A Square in a Triangle

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Edited by Richard Walker, Friday, 2 Oct 2020, 09:23

This is a Sangaku-like puzzle (see https://learn1.open.ac.uk/mod/oublog/viewpost.php?post=230691)

We have a square inscribed in a triangle of known base b and height h, as shown. What is the length s of the square's side?

I called this a Samurai puzzle because many of the original sangaku were the work of Samurai.

(Solution in Comments.)

Permalink 2 comments (latest comment by Richard Walker, Thursday, 1 Oct 2020, 23:34)
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