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# k-man

Member Since --
Offline Last Active Today, 08:58 PM

### #342030A triangle defined by cevians

Posted by on 02 April 2015 - 10:44 PM

another proof

1) draw 3 additional lines parallel to each cevian passing through the remaining vertices of 2 triangles.

2) show that 6 other shaded triangles are mirror images of the green triangle and therefore have the same area

3) show that every part of a shaded triangle that lies outside of the big triangle has an equal unshaded part inside the big triangle. Midpoints of big triangle's sides are points of symmetry.

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### #341574Line segments and the conservation of space

Posted by on 13 February 2015 - 06:44 PM

Spoiler for like this

but how do you 'know' these can't be further optimized?

Well.... I guess I don't.

Spoiler for but let me think

Your assumption (highlighted in the quote) is not that difficult to prove.

Spoiler for

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### #341533Polygons make a line

Posted by on 10 February 2015 - 06:25 PM

Using the interpretation of "crossing" as "having a common point with"...

Spoiler for there are an infinite number of such straight lines

k-man always has such elegant solutions to these problems. I'm sorry but I couldn't contain myself.

Thanks, gavinksong, but the real credit should be given to BMAD for posting these great puzzles.

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### #341520Black and white square table

Posted by on 09 February 2015 - 03:52 PM

Spoiler for I think

Is this claim for any nxm table or only when n = m ?

For any nxm. I don't have a rigorous proof, but I think it would go along these lines...

Spoiler for outline of a proof

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### #341477Polygons make a line

Posted by on 30 January 2015 - 09:03 PM

Using the interpretation of "crossing" as "having a common point with"...

Spoiler for there are an infinite number of such straight lines

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### #341102Five circles and common points

Posted by on 18 November 2014 - 11:38 PM

Spoiler for for circles

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### #341040Alice and Bob's marathon

Posted by on 12 November 2014 - 05:16 PM

Spoiler for Alice sets the world speed record

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### #339897Weighing machines

Posted by on 02 September 2014 - 08:05 PM

If the caretaker remembers 5 eggs which he might have swapped two of them,

(5c2) or 10 possible combinations,how he could find the pair with 2 trials?

Spoiler for for 5 eggs, it's easy with digital scale

I started working out a similar solution for 10, but didn't have enough time to finish it yet. I'm trying to do it in 3 weighings using a digital scale, but so far, looks like it will require 4. Maybe a combination of digital/balance could be optimal. Is it allowed?

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### #338968Brain game from computer science

Posted by on 08 July 2014 - 05:06 PM

Spoiler for solution

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### #338705First 2014 puzzle. Dissection of a triangle

Posted by on 23 June 2014 - 05:03 PM

Spoiler for Aha!

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### #338553Pairing points

Posted by on 03 June 2014 - 07:07 PM

Spoiler for clarification with the drawing

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### #337735Bake it

Posted by on 07 March 2014 - 08:47 PM

Spoiler for Do you mean like this?

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### #330512Between six towns

Posted by on 10 April 2013 - 07:21 PM

I think you should mark this as solved. There is no way to place 6 points on a surface in a way that the minimum distance between any 2 points was m and the maximum distance between any 2 points was m*sqrt(3).

Spoiler for Informal proof that you can do at most 5

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### #329646Guess the Numbers

Posted by on 14 March 2013 - 04:15 PM

Spoiler for I think

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### #328241Matryoshka

Posted by on 13 February 2013 - 09:57 PM

Spoiler for possible arrangement

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