The passtune is the 5-note tune that opens the castle drawbridge. It is composed of the 7 diatonic notes: A, B, C, D, E, F, G. H is also accepted, and is equivalent to B; this comes from German musical notation, in which B is called H and B flat is called B.

It can be given to you by your god when praying, or discovered through a game of mastermind. Playing a tune on a musical instrument when standing near the drawbridge will give you a clue: hearing a tumbler click means you have a correct note in the wrong place, and hearing a gear turn means you have a correct note in the correct place.

## The brute force solution

The most intuitive way of solving is to use 7 guesses to discover what notes are in the passtune:

```AAAAA
BBBBB
CCCCC
DDDDD
EEEEE
FFFFF
GGGGG
```

You may not need to use all these guesses to discover how many of which notes you need (in fact you will need at most 6: if you know the tune contains only A's after trying down to FFFFF, then it must also contain a G).

Imagine you have discovered the passtune contains an A, a B, a C, and 2 G's.

Choose an unused letter, D, and try to find where the A is:

```ADDDD
DDDDA
```

If the fourth guess here yields a turning gear, you know the A must be in the fourth position. Repeat this process for B, but with the known A in place:

```BDDAD
DDDAB
```

If the first guess here yields two turning gears, you know the B must be in the first position. Repeat this process for C, but with the known A and B in place:

```BCDAD
BDDAC
```

If the third guess here yields three turning gears, you know the C must be in the third position.

Because G is present twice, you know that the remaining two unknown letters must both be G, and so the passtune is BGGAC.

This method uses at most 16 guesses.

## The slightly clever solution

The idea here is the same as above, but you make guesses as you discover information, as shown in the example below:

First guess AAAAA. If no gears turn, try BBBBB, then CCCCC, and you will find a letter which is present in the solution, say, A.

Now guess that A is in the first position, and try to discover whether the solution contains B:

```ABBBB
```

If two tumblers click, the first position must be B, so next guess that A is in the second position and that there are C's:

```BACCC
```

If two tumblers click and one gear turns, the second position must be C, so next guess that A is in the third position and that there are D's:

```BCADD
```

If one tumbler clicks and two gears turn, you know the A can't be in the third position and that there are no D's, so try:

```BCEAE
```

If one tumbler clicks and two gears turn, you know the A can't be in the fourth position and that there are no E's, so try:

```BCFFA
```

If three gears turn, you know there are no F's, so the solution must be:

```BCGGA
```

This method is faster than the intuitive one, but requires some thought.

## The best solution

A number of schemes for solving general mastermind games are known, such as this one, which requires random guesses, but on average only a small number of them.