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## instructions

Each of the following puzzles consists of a diagram of an ancient Greek temple. Starting from an entrance (marked with the letter 'e'), your goal is to find a path to the altar, stepping from square to square. For an additional challenge, try to find a way back to the entrance to leave the temple.

Every square is marked with a symbol. Each time you move from one square to the next, the orientation of the gateways (the bold, black lines between some of the squares) is changed according to a chart. For example, moving from a beta square to an alpha square might change the gateways, either opening them if they were closed, or closing them if they were open.

The gateways are always initially closed. You can only move to adjacent squares. You cannot move diagonally, jump over squares, pass through walls, or pass through gateways that are closed. Moving from an entrance to another square, alpha or beta, has no effect on the orientation of the gateways.

## example

Let's examine the above example puzzle with a few different possible sets of rules. We'll use the following notation to show where we are, as well as the orientation of the gateways.

 Start on left tile. Gateways start closed. Move to middle tile. Moving from alpha to beta, gateways open. Move through open gateway to right tile. Moving from beta to alpha, gateways change position. Since the gateway was open, it closes behind you.

With these rules, you can make it to the altar, but you can't get back out! Moving to the middle tile opens the gateway, and then moving to the right tile closes the gateway behind you.

Now let's see what happens when we apply another possible set of rules for this hallway:

 Start on left tile. Gateways start closed. Move to middle tile. Moving from alpha to beta, gateways stay the same. Since the gateway was closed, it remains closed.

Uh oh. Now moving to the middle tile no longer opens the gateway. However, there is still hope. Notice that moving from a beta tile to an alpha tile will open the gateways. You can't move to the right alpha tile, since it is blocked by the closed gateway. However, you could go back to the left alpha tile...

 Move back to left tile. Moving from beta to alpha, gateways open. Move to middle tile. Moving from alpha to beta, gateways stay the same. Since the gateway was open, it remains open. Move through open gateway to right tile. Moving from beta to alpha, gateways open. Since the gateway was already open, it remains open.

Unlike the last set of rules, now the gateway stays open when we move to the right tile. This means that we can proceed back out after reaching the altar:

 Start on right tile. Gateways are open. Move to middle tile. Moving from alpha to beta, gateways stay the same. Since the gateway was open, it remains open. Move to left tile. Moving from beta to alpha, gateways open. Since the gateway was open, it remains open.

And we're out. With this set of rules, once the gateway was opened, it stayed opened.

Now let's see what happens when we apply one last possible set of rules for this hallway:

 Start on left tile. Gateways start closed. Move to middle tile. Moving from alpha to beta, gateways close. Since the gateway was closed, it remains closed.

Once again, we have the problem of a closed gateway getting in our way. Let's try the same trick as last time, moving back to the left alpha tile:

 Move back to left tile. Moving from beta to alpha, gateways change. Since the gateway was closed, it now opens. Success! Move to middle tile. Moving from alpha to beta, gateways close.

Whoops. Under this set of rules, moving from an alpha tile to a beta tile always closes the gateways, no matter what. With this set of rules, this passage to the altar is simply impassable.

## solving tips

Each of the following puzzles has a different set of rules, so think carefully about how combinations of moves (alpha to beta, beta to alpha, alpha to alpha, beta to beta) will affect the gateways.

As we saw above, moving back and forth between squares may help change the state of the gateways. It may be necessary to go to parts of the temple that may seem out of your way but are actually aligning your steps and the position of the gateways for future moves.