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Mar 7, 2021, 1:02:42 PM3/7/21

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Hello, all

I am stuck at the Master-Mind-like puzzle from Journeyman

Project, where the player must find a sequence of three

*different* colors out of five available, in five attempts,

so that there are 60 combinations to choose from. In re-

sponse to each guess, he receives the number of matching

items, which have the right color at the right position. To

complicate matters, the puzzle has to be solved within a

very short time limit.

Has anybody an idea how to make it honestly, without the as-

sistance of a computer program that keeps track of exlcuded

combinations and suggests a next attempt that efficiently

narrows-down the remaning possiblities? I can't find a

strategy simple enough to employ in mind & memory.

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I am stuck at the Master-Mind-like puzzle from Journeyman

Project, where the player must find a sequence of three

*different* colors out of five available, in five attempts,

so that there are 60 combinations to choose from. In re-

sponse to each guess, he receives the number of matching

items, which have the right color at the right position. To

complicate matters, the puzzle has to be solved within a

very short time limit.

Has anybody an idea how to make it honestly, without the as-

sistance of a computer program that keeps track of exlcuded

combinations and suggests a next attempt that efficiently

narrows-down the remaning possiblities? I can't find a

strategy simple enough to employ in mind & memory.

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Mar 10, 2021, 7:57:13 PM3/10/21

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Let’s start with five colors represented by a, b, c, d and e.

There are 10 possible choices for the three colors not counting positioning.

I would list the ten cases and then cross them off when they are eliminated.

How can we find the colors? (I’ll talk about position strategies in another post.)

If we give some version of (abc) for Guess 1,

Case 1: three correct colors - the colors are (abc).

Case 2: one correct color - the colors are (ade), (bde) or (cde).

Case 3: two correct colors - the colors are

(abd), (abe), (acd), (ace), (bcd) or (bce).

For Case 1, you have the colors and one set of position information. I think you know how solve this one for positions too.

For Case 2, you have three possible choices for the colors, you should know which one of the three it is after the third Guess. (Guess 2 (ade) if it is not (ade) then Guess 3 (bde) if it not (bde) then it is (cde).)

For Case 3, you have six possible choices for the colors. Guess 2 (abd)

Case 4: three correct colors – (abd) is the answer

Case 5: one correct color – the answer is (ace) or (bce). (Guess 3 (ace) if it is not then it is (bce))

Case 6: two correct colors – the answer is (abe), (acd) or (bcd). (Guess 3 (abe) if not then Guess 4 (acd) if not then (bcd).

So in every case we can get identify the three colors within five guesses.

L. Flynn

Mar 12, 2021, 6:01:00 AM3/12/21

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leflynn:

> LetТs start with five colors represented by a, b, c, d and

easier. I still, however, am at a loss about solving the

original problem as fast as the game requires.

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> LetТs start with five colors represented by a, b, c, d and

> e. There are 10 possible choices for the three colors not

> counting positioning. I would list the ten cases and then

> cross them off when they are eliminated.

Yes, finding a combination instead of a permutation is much
> counting positioning. I would list the ten cases and then

> cross them off when they are eliminated.

easier. I still, however, am at a loss about solving the

original problem as fast as the game requires.

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Mar 14, 2021, 6:39:37 PM3/14/21

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On Sunday, March 14, 2021 at 5:51:31 PM UTC-4, leflynn wrote:

I see finding a combination as part of the problem fortunately, you can do both at once.

When I play mastermind I keep a grid of the possible locations for the remaining colors.

It would start as

a a a

b b b

c c c

d d d

e e e

Rows would be removed or crossed out as colors were eliminated and x’s would be placed in positons that are not allowed. Some obvious results:

Guess results with one correct color either tell us where the three colors present in the guess may go or where they cannot go. For example if Guess 1 (abc) had one correct color and it was not in the correct positon, the position chart would become:

x a a

b x b

c c x

d d d

e e e

When I play mastermind I keep a grid of the possible locations for the remaining colors.

It would start as

a a a

b b b

c c c

d d d

e e e

Rows would be removed or crossed out as colors were eliminated and x’s would be placed in positons that are not allowed. Some obvious results:

Guess results with one correct color either tell us where the three colors present in the guess may go or where they cannot go. For example if Guess 1 (abc) had one correct color and it was not in the correct positon, the position chart would become:

x a a

b x b

c c x

d d d

e e e

Mar 14, 2021, 7:05:37 PM3/14/21

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On Sunday, March 14, 2021 at 5:51:31 PM UTC-4, leflynn wrote:

> On Friday, March 12, 2021 at 6:01:00 AM UTC-5, Anton Shepelev wrote:

> On Friday, March 12, 2021 at 6:01:00 AM UTC-5, Anton Shepelev wrote:

> I see finding a combination as part of the problem fortunately, you can do both at once.

>

> Here is a decision table. You'll need to view it with a fixed width font.
>

Well, that post turned into a mess...

_G1___G2___G3___G4___G5

(ABC)_

_3p0_(BCA)(CAB)

_3p1_(ACB)(BAC)(CBA)

_2p0_(BAD)

______3p1_(BDA)(DAB)

______2p0_(CDA)

___________3p0_(DCA)

___________2p0_(DCB)

___________2p2_(CDB)

______2p1_(BEA)

___________3p0_(EAB)

______2p2_(BAE)(BCD)(CAD)

______1p0_(CEA)_

___________3p1_(ECA)

___________2p0_(ECB)

___________2p2_(CEB)

______1p1_(CAE)(BCE)

_2p1_(ADB)

______3p0_(DBA)

______2p0_(CBD)

___________3p0_(BDC)

___________1p0_(DAC)

___________1p1_(EBA)_

______2p1_(ACD)

______2p2_(AEB)

______1p0_(BEC)

___________3p0_(CBE)

___________2p1_(EAC)

______1p1_(ACE)

_2p2_(ABD)

______2p2_(ABE)

______2p1_(ADC)(DBC)

______1p1_(AEC)(EBC)

_1p0_(DAE)

______3p0_(EDA)

______3p1_(DEA)(EAD)

______2p0_(BED)

___________3p0_(EDB)

___________3p1_(DEB)

___________2p0_(ECD)

___________2p2_(CED)

______2p1_(BDE)(CDE)

______2p2_(DCE)

_1p1_(ADE)_

______3p1_(AED)

______2p0_(DEC)(EBD)

______2p1_(DBE)(EDC)

> Is (DCE) in the correct place?

> Guess1(ABC) 1p0; Guess2(DAE) 2p2; Guess3 (DCE)

> Is (CAD) in the correct place?

> Guess1(ABC) 2p0; Guess2(BAD) 2p2; Guess3(BAE) 1P; Guess4(BCD) 2p1; Guess5(CAD)

Mar 15, 2021, 7:41:19 AM3/15/21

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leflynn:

> Well, that post turned into a mess...

Not at all: http://al.howardknight.net/?ID=161580839200

but I still wonder why anyone who knows about monospace

fonts should access Usenet via crippled GoogleGropus...

I have not yet studied your solution yet, but will do.

> Well, that post turned into a mess...

but I still wonder why anyone who knows about monospace

fonts should access Usenet via crippled GoogleGropus...

I have not yet studied your solution yet, but will do.

Mar 15, 2021, 12:51:10 PM3/15/21

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The solution I gave picks from the available responses at each stage in alphabetical order. It’s not the way I would play a real game. When I play Mastermind, I keep piles of colors with information in my head.

For colors here, I start with A,B,C.

If all three are right, then good.

If one is right, then D and E are colors and one of A,B,C. My round two guesses for these cases use A,D,E.

(If your guess is always three distinct colors, then one color right always tells you that the other two are good colors. Once you know two for sure, every guess either tells you that one of the other three colors is right or wrong.)

If two are right, then I would have a pile of A,B,C and remember that my answer needs two of them and a pile of D,E and I need one of them.

My round two guess for these cases use A,B,D for colors.

For round three

If your A,B,D guess has one color right, then you know C and E and are correct and one A and B. I chose to check A,C,E first

If you’re A,B,D guess has two colors right, then you either need to swap A or B for C or you need to swap D for E. I chose to swap B for C and guess using A,C,D. You can tell right away by whether number of correct colors stayed the same, decreased or increased whether the B -> C swapped good for good (B,C is right and so is D), good for bad (A,B is right and so is E) or bad for good (A,C is right and so is D).

For positions, I just choose the first one alphabetically to go in the earliest correct position or not go in the earliest wrong position working through to the current guess, and then move on to the next color.

L. Flynn

Mar 16, 2021, 1:55:06 PM3/16/21

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leflynn:

> Here is a decision table.

If I understand your notation, xpy encodes a guess with x

correct colors and y colors at the correct position. I fear

it is not the feedback the player receives in the puzzle I

posted. Instead of two numbers, the machine answers to each

guess with a single number -- the quanitity of colors at

correct positions. It does not reveal how many colors in the

guess are present in the sought combination at incorrect po-

sitions. I wrote in my original post:

> In response to each guess, he receives the number of

screenshot would help:

https://freeshell.de/~antonius/img_host/colorpuzzle.png

The five avaialbe colors are present above label that reads

"possible color synapse nodes". The guess log is on the

right, with a single number annotating each of the four

spend guesses: 0,1,0,1. This is not a binary code, but the

nubmers of matching color-positions.

> Here is a decision table.

correct colors and y colors at the correct position. I fear

it is not the feedback the player receives in the puzzle I

posted. Instead of two numbers, the machine answers to each

guess with a single number -- the quanitity of colors at

correct positions. It does not reveal how many colors in the

guess are present in the sought combination at incorrect po-

sitions. I wrote in my original post:

> In response to each guess, he receives the number of

> matching items, which have the right color at the right

> position.

I am sorry that my English was not clear enough. Perhaps a
> position.

screenshot would help:

https://freeshell.de/~antonius/img_host/colorpuzzle.png

The five avaialbe colors are present above label that reads

"possible color synapse nodes". The guess log is on the

right, with a single number annotating each of the four

spend guesses: 0,1,0,1. This is not a binary code, but the

nubmers of matching color-positions.

Mar 16, 2021, 2:20:37 PM3/16/21

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L. Flynn

Message has been deleted

Mar 17, 2021, 6:46:07 PM3/17/21

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On Sunday, March 7, 2021 at 1:02:42 PM UTC-5, Anton Shepelev wrote:

It's essentially a printout of a computer program, so it doesn't even meet that limiting part of your request.

I see some patterns and choices but by the third round it's too messy.

G1 G2 G3 G4 G5

123

_0_231

____0_314

_______0_542

__________1_452

_______1_342

__________0_415

__________1_412 x512

__________2_345 x352

_______2_315

__________1_354 x514

__________2_312

____1_541

_______0_215

__________0_432

__________1_254 x435

__________2_214

_______1_531 x (only non-feasible guess)

__________0_245

__________1_351 x451

__________2_532 x534

_______2_341

____2_531

_______1_234

__________1_241 x251

__________2_235

_______2_431

_1_543

____0_425

_______0_134

__________1_152

__________2_132 x154

_______1_321

__________0_135

__________2_324

_______2_325

__________1_421

____1_253

_______0_524

__________0_142 x145

__________2_521

_______1_413

_______2_213

__________1_453

____2_513

_______1_243

_2_124

____1_523

_______1_143

__________2_153

_______2_423

____2_125

Mar 21, 2021, 10:50:34 AM3/21/21

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Lawrence E Flynn:

> Ouch. Sorry, I've been solving the Mastermind problem, not

> yours.

You indeed have.

> I don't have one I would want to memorize but I have a

> table that wins 51/60 times for an individual puzzle.

> It's essentially a printout of a computer program, so it

> doesn't even meet that limiting part of your request. I

> see some patterns and choices but by the third round it's

> too messy.

Thank you very much anyway. It helped me solve the puzzle

two times! It is randomly generated and the first time I

didn't save my game correctly. I will propose your decision

tree to for inclusion into an existing walkthrough, if I

find a way to do it, with due credits.

> Ouch. Sorry, I've been solving the Mastermind problem, not

> yours.

> I don't have one I would want to memorize but I have a

> table that wins 51/60 times for an individual puzzle.

> It's essentially a printout of a computer program, so it

> doesn't even meet that limiting part of your request. I

> see some patterns and choices but by the third round it's

> too messy.

two times! It is randomly generated and the first time I

didn't save my game correctly. I will propose your decision

tree to for inclusion into an existing walkthrough, if I

find a way to do it, with due credits.

Mar 21, 2021, 12:46:54 PM3/21/21

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The approach I gave is probably not optimal. It was not an exhaustive search.

One question, are you only allowed to make guesses with three different colors,

or could you guess, for example, (A,A,B)?

L. Flynn

Mar 21, 2021, 1:38:24 PM3/21/21

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Lawrence E Flynn:

> The approach I gave is probably not optimal. It was not an

> exhaustive search.

I suspected it, because the walkthrough gives a higher

chance of winning thatn 51/60.

> One question, are you only allowed to make guesses with

> three different colors, or could you guess, for example,

> (A,A,B)?

No, I am not, and nor are any other players :-)

I have thought of writing a program that at every step

chooses a guess that invalidates the most combinations, by

brutally trying every one of them.

> The approach I gave is probably not optimal. It was not an

> exhaustive search.

chance of winning thatn 51/60.

> One question, are you only allowed to make guesses with

> three different colors, or could you guess, for example,

> (A,A,B)?

I have thought of writing a program that at every step

chooses a guess that invalidates the most combinations, by

brutally trying every one of them.

Apr 4, 2021, 10:06:01 AM4/4/21

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Part of the approach I used looks at trying to minimize the maximum number of possible choices in in each of the branches of possible answers (0, 1, 2, or 3 correct) from the current guess given the solution subset for the responses so far. It is usually the 0 and 1 sets that are competing in size, although, once we have a 2 response from then on it is the 1 and 2 sets that compete.

L. Flynn

Apr 7, 2021, 9:30:00 PM4/7/21

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I have an improvement for the cases where the initial guess has zero hits. It only loses three of those 32 cases. It uses two guesses that are not in the possible solution set at the point they are used.

G1 G2 G3 G4 G5

123

_0_412
123

____0_235

_______0_354

__________0_541

__________1_341

__________2_351

_______1_241

__________0_534

__________1_254 x531 x345

__________2_251

_______2_134 (not a possible solution at this point)

__________0_245

__________1_231

__________2_234

____1_314

_______0_431

__________0_542

__________1_532

__________2_435 x451

_______1_142 (not a possible solution at this point)

__________0_215

__________1_352

__________2_342

_______2_214

__________1_315

__________2_514

____2_312

_______1_432

__________1_415

__________2_452

_______2_512

L. Flynn

Apr 8, 2021, 12:59:33 AM4/8/21

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G1 G2 G3 G4 G5

123

_1_134
123

____0_413

_______0_325

__________1_521

__________2_321

_______1_253

__________0_421 x425

__________1_543

__________2_243

_______2_213

__________1_453

__________2_513

____1_124 NP

_______1_145

__________1_152

__________2_142

_______2_324

__________2_524

____2_135

_______1_154

_______2_132

Apr 9, 2021, 9:59:47 AM4/9/21

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L. Flynn:

> Anton,

> I have an improvement for the cases where the initial

> guess has zero hits. It only loses three of those 32

> cases. It uses two guesses that are not in the possible

> solution set at the point they are used.

> [...]
> Anton,

> I have an improvement for the cases where the initial

> guess has zero hits. It only loses three of those 32

> cases. It uses two guesses that are not in the possible

> solution set at the point they are used.

> And an improvement where the first guess has one hit that

> loses one out of 21.

I have already solved the puzzle with the help of your initial
> loses one out of 21.

decision tree. If you will care to provide the entire

decision tree with these improvements, then I will update it

in the walkthrough on this WIKI:

https://strategywiki.org/wiki/The_Journeyman_Project:_Pegasus_Prime/Morimoto_Colony#Shield_Generator

https://pastebin.com/raw/NCnpAz3s

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Apr 9, 2021, 1:52:26 PM4/9/21

to

An improved tree that gets to the answer 56/60 times. The ##Y and ##X are my checks on success or failure for the list of 60 possible answers in numerical order. The odds of winning all of the games in a five-game match is slightly over 70%. It gets to the answer for 30 of the cases with four or fewer guesses.

L. Flynn

____G1 G2 G3 G4 G5

01Y123

37Y_0_412

18Y____0_235

33Y_______0_354

58Y__________0_541

31Y__________1_341

34Y__________2_351

19Y_______1_241

57Y__________0_534

24Y__________1_254 55X531 36X345 28

22Y__________2_251

16Y_______2_231

21Y__________1_245

17Y__________2_234

26Y____1_314

43Y_______0_431

59Y__________0_542

56Y__________1_532

45Y__________2_435 46X451

35Y_______1_352

15Y__________0_215

32Y__________2_342

14Y_______2_214

27Y__________1_315

51Y__________2_514

25Y____2_312

44Y_______1_432

39Y__________1_415

47Y__________2_452

49Y_______2_512

05Y_1_134

38Y____0_413

30Y_______0_325

52Y__________1_521

28Y__________2_321

23Y_______1_253

40Y__________0_421 42X425

60Y__________1_543

20Y__________2_243

13Y_______2_213

48Y__________1_453

50Y__________2_513

09Y____1_145

29Y_______0_324

54Y__________2_524

10Y_______1_152

07Y_______2_142

06Y____2_135

12Y_______1_154

04Y_______2_132

02Y_2_124

53Y____1_523

08Y_______1_143

11Y__________2_153

41Y_______2_423

03Y____2_125

L. Flynn

____G1 G2 G3 G4 G5

01Y123

37Y_0_412

18Y____0_235

33Y_______0_354

58Y__________0_541

31Y__________1_341

34Y__________2_351

19Y_______1_241

57Y__________0_534

24Y__________1_254 55X531 36X345 28

22Y__________2_251

16Y_______2_231

21Y__________1_245

17Y__________2_234

26Y____1_314

43Y_______0_431

59Y__________0_542

56Y__________1_532

45Y__________2_435 46X451

35Y_______1_352

15Y__________0_215

32Y__________2_342

14Y_______2_214

27Y__________1_315

51Y__________2_514

25Y____2_312

44Y_______1_432

39Y__________1_415

47Y__________2_452

49Y_______2_512

05Y_1_134

38Y____0_413

30Y_______0_325

52Y__________1_521

28Y__________2_321

23Y_______1_253

40Y__________0_421 42X425

60Y__________1_543

20Y__________2_243

13Y_______2_213

48Y__________1_453

50Y__________2_513

09Y____1_145

29Y_______0_324

54Y__________2_524

10Y_______1_152

07Y_______2_142

06Y____2_135

12Y_______1_154

04Y_______2_132

02Y_2_124

53Y____1_523

08Y_______1_143

11Y__________2_153

41Y_______2_423

03Y____2_125

Apr 13, 2021, 4:16:42 PM4/13/21

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On Monday, March 8, 2021 at 1:02:42 AM UTC+7, Anton Shepelev wrote:

> Hello, all

>

> I am stuck at the Master-Mind-like puzzle ...
> Hello, all

>

Better yet, try this webpage:

https://james.fabpedigree.com/mmind/mmind.htm

Five pegs, seven colors. Pretty tough! How many guesses do you need?

Although details are little known, it's always possible to solve with six guesses.

At the webpage you can go for computer's secret, have it go for yours, or both concurrently.

Try it and tell me what you think.

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May 3, 2021, 6:23:06 AM5/3/21

to

L. Flynn:

> An improved tree that gets to the answer 56/60 times. The

> ##Y and ##X are my checks on success or failure for the

> list of 60 possible answers in numerical order. The odds

> of winning all of the games in a five-game match is

> slightly over 70%. It gets to the answer for 30 of the

> cases with four or fewer guesses.

Thanks for an improved solution. Hopefully I will get around

to updating the game's walkthrough.

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> An improved tree that gets to the answer 56/60 times. The

> ##Y and ##X are my checks on success or failure for the

> list of 60 possible answers in numerical order. The odds

> of winning all of the games in a five-game match is

> slightly over 70%. It gets to the answer for 30 of the

> cases with four or fewer guesses.

to updating the game's walkthrough.

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Jul 7, 2021, 3:31:52 PM7/7/21

to

On Friday, April 9, 2021 at 1:52:26 PM UTC-4, leflynn wrote:

> An improved tree that gets to the answer 56/60 times. The ##Y and ##X are my checks on success or failure for the list of 60 possible answers in numerical order. The odds of winning all of the games in a five-game match is slightly over 70%. It gets to the answer for 30 of the cases with four or fewer guesses.

> L. Flynn

Here is a version that is converted from colors 1-5 to colors YBGPR
> An improved tree that gets to the answer 56/60 times. The ##Y and ##X are my checks on success or failure for the list of 60 possible answers in numerical order. The odds of winning all of the games in a five-game match is slightly over 70%. It gets to the answer for 30 of the cases with four or fewer guesses.

> L. Flynn

G1 G2 G3 G4 G5

YBG
_0_PYB

____0_BGR

_______0_GRP

__________0_RPY

__________1_GPY

__________2_GRY

_______1_BPY

__________0_RGP

__________1_BRP RGY GPR

__________2_BRY

_______2_BGY

__________1_BPR

__________2_BGP

____1_GYP

_______0_PGY

__________0_RPB

__________1_RGB

__________2_PGR PRY

_______1_GRB

__________0_BYR

__________2_GPB

_______2_BYP

__________1_GYR

__________2_RYP

____2_GYB

_______1_PGB

__________1_PYR

__________2_PRB

_______2_RYB

_1_YGP

____0_PYG

_______0_GBR

__________1_RBY

__________2_GBY

_______1_BRG

__________0_PBY PBR

__________1_RPG

__________2_BPG

_______2_BYG

__________1_PRG

__________2_RYG

____1_YPR

_______0_GBP

__________2_RBP

_______1_YRB

_______2_YPB

____2_YGR

_______1_YRP

_______2_YGB

_2_YBP

____1_RBG

_______1_YPG

__________2_YRG

_______2_PBG

____2_YBR

Jul 13, 2021, 12:35:24 PM7/13/21

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L. Flynn:

> Here is a version that is converted from colors 1-5 to colors YBGPR

That makes more sense, thank you. I can use it now with less work.
> Here is a version that is converted from colors 1-5 to colors YBGPR

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