Passtune - Revision history

Gorgor: replacing a with 1 to reduce confusion

2019-10-29T13:33:00Z

replacing a with 1 to reduce confusion

62.4.105.221 at 19:34, 1 March 2016

2016-03-01T19:34:04Z

Bcode: wikipedia interwiki

2013-02-07T20:08:23Z

wikipedia interwiki

84.150.173.142: Corrected broken link to mastermind solver

2008-08-15T11:34:24Z

Corrected broken link to mastermind solver

84.16.37.186: Corrected the German notation explanation in the first paragraph.

2008-05-31T21:29:47Z

Corrected the German notation explanation in the first paragraph.

Ray Chason: H is understood as B

2008-05-08T02:42:27Z

H is understood as B

ZeroOne: /* External links */ added [http://www.gridbug.de/mm.html Opening the Castle's Drawbridge playing Mastermind] — An online passtune solver

2006-12-20T16:22:31Z

‎External links: added [http://www.gridbug.de/mm.html Opening the Castle's Drawbridge playing Mastermind] — An online passtune solver

Eidolos: Add the link to my NetHack Mastermind page.. I'd include the info wholesale but this article is long enough

2006-11-14T17:35:32Z

Add the link to my NetHack Mastermind page.. I'd include the info wholesale but this article is long enough

ZeroOne: changed "intuitive" to "brute force"... added see also: *wikipedia:Mastermind (board game)

2006-07-20T01:20:11Z

changed "intuitive" to "brute force"... added see also: *wikipedia:Mastermind (board game)

Jayt: tips for solving mastermind

2006-07-20T00:04:47Z

tips for solving mastermind

New page

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.

It can be given to you by your [[god]] when [[pray|praying]], or discovered through a game of [http://en.wikipedia.org/wiki/Mastermind_%28board_game%29 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 intuitive 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
DADDD
DDADD
DDDAD
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
DBDAD
DDBAD
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
BDCAD
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 [http://web.archive.org/web/20030218014634/http://www.csc.ncsu.edu/degrees/undergrad/Reports/rtrosu/heuristic.htm this one], which requires random guesses, but on average only a small number of them.

[[Category:Strategy]]

@@ Line 1: / Line 1: @@
 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 [[pray|praying]], or discovered through a game of [[wikipedia:Mastermind (board game)|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.
+It can be given to you by your [[god]] when [[pray|praying]], or discovered through a game of [[wikipedia:Mastermind (board game)|mastermind]]. Playing a tune on a tonal [[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==

@@ Line 1: / Line 1: @@
 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 [[pray|praying]], or discovered through a game of [http://en.wikipedia.org/wiki/Mastermind_%28board_game%29 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.
+It can be given to you by your [[god]] when [[pray|praying]], or discovered through a game of [[wikipedia:Mastermind (board game)|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==

@@ Line 83: / Line 83: @@
 ==External links==
-*[http://www.gridbug.de/mm.html Opening the Castle's Drawbridge playing Mastermind] &mdash; An online passtune solver
+*[http://nethack.gridbug.de/mm.html Opening the Castle's Drawbridge playing Mastermind] &mdash; An online passtune solver
 *[[wikipedia:Mastermind (board game)]]
 *[http://sartak.katron.org/nh/mastermind/ Botting NetHack's Mastermind]

← Older revision		Revision as of 21:29, 31 May 2008
Line 1:		Line 1:
−	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 flat is called H.	+	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 [[pray\|praying]], or discovered through a game of [http://en.wikipedia.org/wiki/Mastermind_%28board_game%29 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.		It can be given to you by your [[god]] when [[pray\|praying]], or discovered through a game of [http://en.wikipedia.org/wiki/Mastermind_%28board_game%29 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.

@@ Line 82: / Line 82: @@
 A number of schemes for solving general mastermind games are known, such as [http://web.archive.org/web/20030218014634/http://www.csc.ncsu.edu/degrees/undergrad/Reports/rtrosu/heuristic.htm this one], which requires random guesses, but on average only a small number of them.
-==See also==
+==External links==
 *[[wikipedia:Mastermind (board game)]]
 *[http://sartak.katron.org/nh/mastermind/ Botting NetHack's Mastermind]
 [[Category:Strategy]]

@@ Line 17: / Line 17: @@
 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.
+Imagine you have discovered the passtune contains 1 A, 1 B, 1 C, and 2 G's.
 Choose an unused letter, D, and try to find where the A is: