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Spinning Column Puzzle

This week we will have only a logic/math puzzle. Here it is. Fair warning it is pretty hard.

Question

You are trapped in a tomb. Inside the tomb there is a pillar about 1 foot in diameter. About a shoulder-high height from the floor are four holes in the pillar that are evenly spaced around the column. The holes are barely big enough to fit your hand in. Inside each hole is a switch that can either be in the up or down position. The goal is to get all the switches in the same position.

You may stick both your hands in any two holes at the same time and switch the switches at the same time. You must then take your hands out. If the switches are then all in the same position, then a door will open leading to freedom. Otherwise, the pilar will spin around randomly, but without changing the switches.

You are allowed up to four attempts. If you fail, you will be trapped in the tomb forever. How can you guarantee your freedom?

Answer

For purposes of discussion, let:

U = Switch in up position

D = Switch in down position.

  1. For turn 1, choose opposite switches. If the same, flip both switches. If opposite, flip the D switch.
  2. For turn 2, choose opposite switches.
  3. If the turn 1 switches were originally in the same position, and the turn 2 switches are in the same position, then flip either switch on turn 2. This will result in either the puzzle being solved or switches in an UUDD configuration.
  4. If the turn 1 switches were originally both up, and the turn 2 switches are in opposite positions, then flip the up switch. This will result in the puzzle being solved in a DDDD configuration.
  5. If the turn 1 switches were originally both down, and the turn 2 switches are in opposite positions, then flip the down switch. This will result in the puzzle being solved in the UUUU configuration.
  6. If the turn 1 switches were opposite, and the turn 2 switches are in the same position, then flip either switch. This will either result in a solved puzzle or an UUDD configuration.
  7. If the turn 1 switches were opposite, and the turn 2 switches are in opposite positions, then flip the D switch. This will either result in a solved puzzle in the UUUU configuration.
  8. For turn 3, if the puzzle isn't solved yet, it must be in a UUDD configuration. Pick adjacent switches and flip both. This will result in the puzzle being solved or a UDUD configuration.
  9. For turn 4, pick opposite switches and flip both. This will solve the puzzle.