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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Two kings should be put in the following places:

1) G4 and 2) D1

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.

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

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

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)

Correct – this is the rigth step towards the solution.

I love playing chess, and I support GM Var Akobian. Var took the 1st place in America Open Chess tournaments 3 times. he is considered to be a genoius, and that’s how he has been alled during MTV’s true life. Var is being sponsored by our company called <a href="http://www.betterrankings.com">Better Rankings</a> which specializes in search engine optimization.