Accepted Answer

Hi, I was about to give up on this one but when writing to you to argue it was impossible I argued out the solution :-D

Solution

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Derrivation of the answer

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The red lines shows where we definitely need our shape's edge to 'go along'.

Consider triangle in box 25 (top left one)

That can only be in the shape with either circle in box XX XX XXXXXX in both 24. The other two circles would cause shapes to be isolated.

The circle in box 24 can only be in one shape that contains itself and the triangle in box 25 namely

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Clearly we can only put one more of these shapes in the rest of the grid.

Hence triangle 25 must be with circle 22

Now arises the problem of what triange to pair circle 24 with.

Clearly triangle 7 is no good.

Triangle 10 would require a kind of zig zag shape that would not accommodate triangle XX XXX XXXXXX 18 which must subsequently be paired.

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Hence circle 18 must be paired with triangle 11

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Circle 18 then shows we need a 'sticky out' of two blocks (3 blocks in total). Initially this seemed impossible but then it click and here is the solution

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Got there ;-)

Edited by Ben Brown on 2/5/2009 at 2:10 PM

Expert:	Ben Brown
Pos. Feedback:	100.0 %
Accepts:
Answered:	2/5/2009

Mathematician

First Class Honours in Mathematics from Oxford University