Puzzle: create a Pentagon with rule and compass <EOM>


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 (9)

  1. amit.scorpio3 says:

    Two kings should be put in the following places:

    1) G4 and 2) D1

  2. amit.scorpio3 says:

    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 🙂

  3. Adi Oltean says:

    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.

  4. benvi says:

    White king on f3, black king on h1, then Kxf2++.

  5. Adi Oltean says:

    Yes – that’s the answer for the chess problem!

  6. none supplied says:

    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)

  7. Adi Oltean says:

    Correct – this is the rigth step towards the solution.

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