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Puzzle: create a Pentagon with rule and compass

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The title sums it all.

 

P.S. And, as a Christmas bonus, here is a nice chess puzzle.

image

In the above diagram you must add the two missing kings in such a way that White, who is on the move, can deliver immediate mate, i.e. mate in one move.

[source: ChessBase]

Comments

  1. G4 and 2) D1
  • Anonymous
    December 26, 2007
    Sorry, I forgot to mention the move that should be followed once you have placed two missing kings in correct squares: Place king in the following squares:
  1. G4 and 2) D1 and give a check to Black King by puting black bishop (i.e. bishop in the black square) in D4 square ! King is trapped and cannot move anywhere :)

  • Anonymous
    December 27, 2007
    Amit - not sure if you provided the right coordinates (maybe you meant B1 instead of D1?) - if you move bishop to D4 and the black king is on B1 then you can still move the king to C1.

  • Anonymous
    January 02, 2008
    White king on f3, black king on h1, then Kxf2++.

  • Anonymous
    January 03, 2008
    Yes - that's the answer for the chess problem!

  • Anonymous
    January 04, 2008
    For the pentagon, I assume you mean regular pentagon? with all sides/angles equal etc? In which case, constructing sin 18 or sin 36 or sin 54 or sin 72 should do. sin 18 = (sqrt(5) - 1)/4 sqrt(5) can easily be constructed (hypotenuse of 1,2,sqrt(5) triangle)

  • Anonymous
    January 06, 2008
    Correct - this is the rigth step towards the solution.

  • Anonymous
    January 14, 2008
    The comment has been removed