Tag: Expert

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There are 5 houses and each of them has a different color. Their respective owners have different heritages, drink different types of beverages, smoke different brands of cigarettes, and look after different types of pets. It is known that:

  • The Brit lives in the red house.
  • The Swede keeps dogs as pets.
  • The Dane drinks tea.
  • Looking from in front, the green house is just to the left of the white house.
  • The green house’s owner drinks coffee.
  • The person who smokes Pall Malls raises birds.
  • The owner of the yellow house smokes Dunhill.
  • The man living in the center house drinks milk.
  • The Norwegian lives in the leftmost house.
  • The man who smokes Blends lives next to the one who keeps cats.
  • The man who keeps a horse lives next to the man who smokes Dunhill.
  • The owner who smokes Bluemasters also drinks beer.
  • The German smokes Prince.
  • The Norwegian lives next to the blue house.
  • The man who smokes Blends has a neighbor who drinks water.

The question is, who owns the pet fish?

The German owns the fish. Solution coming soon.

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Design a game which takes less than 35 moves to get to the position below.

Remark: The second board is provided for analysis.

One possible solution is:

1.d3 h6 2.Bxh6 f5 3.Qd2 f4 4.Qxf4 a5 5.Qxc7 Kf7 6.g3 Kg6 7.Bg2 Kh5 8.Bxb7 Kg4 9.Nf3 Kh3 10.Bxc8 e5 11.Bxg7 e4 12.Kd2 e3+ 13.Kxe3 Kg2 14.Ng1 Kf1 15.Kf3 Ke1 16.Qxa5+ Bb4 17.Nc3+ Kd2 18.Rf1 Rh3 19.Bxd7 Nh6 20.Nd1 Kc1 21.Bxh6+ Kb1 22.Bc1 Na6 23.Kg2 Rc8 24.Bxh3 Rc3 25.Nxc3+ Ka1 26.Nb1 Nc5 27.Rd1 Be1 28.Qxe1 Ne4 29.Kf1 Nd2+ 30.Rxd2 Qd5 31.Qd1 Qg2+ 32.Ke1 Qf1+ 33.Bxf1

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Can you design a chess game which ends up with a stalemate in the 10th move?

One possible game is:

1. h4 h5
2. c4 a5
3. Qa4 Ra6
4. Qxa5 Rah6
5. Qxc7 f6
6. Qxd7 Kf7
7. Qxb7 Qd3
8. Qxb8 Qh7
9. Qxc8 Kg6
10. Qe6

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There are a fly and three spiders on the edges of a cube. If the spiders’ velocities are at least 1/3 of the fly’s velocity, and all insects can travel only along the edges of the cube, show that the spiders can eventually catch the fly.

Choose two opposite edges of the cube, then let two of the spiders “protect” them from the fly. You can do this by keeping the distance from the two spiders to the edges’ endpoints at most 1/3 of the distance from the fly to these endpoints. The remaining parts of the cube do not contain any loops, so the third spider can easily catch the fly there.

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White starts and forces Black to mate him in 8 moves.

1. Nb1+ Kb3
2. Qd1+ Rc2
3. Bc1 axb6
4. Ra1 b5
5. Rh1 bxc4
6. Ke1 c3
7. Ng1 f3
8. Bf1 f2#

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It is well known how to split fairly a cake between two people – one of them cuts, the other one picks. The question is, how can you split fairly a cake between three people?

Easy: “Fairly” means that every person gets at least 1/3 of the cake.

Hard: “Fairly” means that every person has the opportunity to get at least as much cake as any other.

Easy (Banach-Knaster method):

The first person cuts 1/3 piece of the cake. If the second person thinks it is larger than 1/3, he can trim it to 1/3. If the third person thinks the cut (and possibly trimmed) piece is larger than 1/3, he can trim it to 1/3 and keep it. Otherwise, the second person takes the piece if he decided to trim it, or the first one, in case he did not. After that, there are two people left, and they can easily split the remaining cake between them. This approach works for any number of people.

Hard (Selfridge-Conway method):

The first person cuts the cake in 3 pieces. The second one takes the biggest piece and trims it so that it becomes as large as the second biggest piece, puts the trimmings aside. The third person picks one of the three big pieces. Then, if the trimmed piece is still available, the second person takes it, if not – he picks whichever he likes. The first person takes the last remaining big piece. Among the first two people, whoever did not pick the trimmed big piece, splits the trimmings into 3 parts. The other one picks one of these parts, then the first person picks another. The last part goes to the person who split the trimmings.