# 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.

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]

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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 ðŸ™‚

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++.

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)