a geometry question - 4

AB = BC = CA
BD = 8
CD = 7
AD = 5
Find the BDA angle.

Answer:
120°
(The solution method other than a "brute force" method eludes me. I prepared this question 12 years ago, and I assume there was an easier method. If anybody knows such a method, let me know at karakusk at yahoo dot com.)

a geometry question - 3

BD =DC and AE = EC given.

Find the unknown angle.

Answer:
20°

a geometry question - 2

Find the unknown angle.

Answer:
70°

a geometry question - 1

Find the unknown angle.

Answer:
130°

a "retro" chess problem

white plays and mates in two.

solution and explanation:

1. fxe6 e.p. f5 2. Bxf5 mate.

the only last possible move of black can be e7-e5. all 16 white pieces are on board so d6xe5 is impossible. e6-e5 is impossible as a black pawn at e6 would have given check. other possible last moves are discarded in a similar way.

the position is legal as far as i can tell. white pawn structure indicates minimum 4 captures and this is possible as there are 9 black pieces on the board.

knights cannot triangulate

white plays and draws.

solution:

1. Kg2 Nb6 2. Kg1 Nd5 3. Kg2 Ne3 4. Kg1 draw...