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Your Yin, My Yang (Posted on 2008-01-19) Difficulty: 3 of 5
Consider a cylinder having the two major halves of the Yin-yang symbol as the profile of two moulded pieces of differently coloured woods.

Allow one of these pieces to be obliquely cut from A to B as in the illustration.

What percentage by volume of the whole cylinder do each of these two parts represent?

The lower part of the illustration attempts to portray a receding void on the left and having cylindrical dimensions against a similar protuberance on the right, and of the same scale.

Also consider the lower section of the graphic to be an 'abbreviated' cross-section of the top, but rotated through 90°. And, if it wasn't obvious, the small black and white circles are to be dismissed from your thoughts.

See The Solution Submitted by brianjn    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Solution Comment 2 of 2 |
(In reply to Solution by Leming)

Leming, when you first saw this proposal I recall that you thought that I was underselling its difficulty.

The difficulty, I think I said at that time was perception rather than mathematics.  May I compliment you on a great break down of the object and assessment of it parts?

I also seem to recall that even then i could have been making an overstatement.

Prior to making public my personal solution, and I do not slight your efforts because I went down that same path.  Shortly afterwards I realised that there was a somewhat more intuitive solution. 

I'll wait a day or two to see if we can get something less formal by way of explanation; don't get me wrong, everything Leming says is inherent in my solution.

  Posted by brianjn on 2008-01-25 03:16:05

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