Mastermind!

Let's start a game of Mastermind! I will start by creating the code, and anyone here can make a guess (we will change next game). Instead of colors, we will use the numbers 1-6, and the same number can be used more than once. You guess a 4-digit code using the numbers 1-6. You will have 12 guesses (put the number by each one), and after each guess I will say how many numbers are correct but in the wrong place, and how many are correct and in the right place.

OK, I got a code (rolled 4d6). Who will be the first one to guess!

Hmmmm.

I will take guess number 1 then.

2 (red), 3 (red), 4 (red), 6 (red)

It's fun when I can pick the numbers to be the same colour!

Numbers correct, wrong place: 2

Numbers correct, right place: 1

Question: could the numbers repeat? Not asking if they do, just if its allowed in the game

Yes, but let’s say you put down X twice, and only one exists, it will say one is right not two.

1156

Ok, then. Guess number 2.

2, 3, 4, 5.

I'll go in order, but I will let Mcbehrer change his if he wants before answering it.

Numbers correct, wrong place: 1

Numbers correct, right place: 0

Summary

G-U-E-S-S: Numbers correct, wrong place/numbers correct, right place

1) 2-3-4-6: 2/1

2) 1-1-5-6: 1/0

Ok, so there's a 6, no 5 or 1.

6, 3, 6, 4

Summary

G-U-E-S-S: Numbers correct, wrong place/numbers correct, right place

1) 2-3-4-6: 2/1

2) 1-1-5-6: 1/0

3) 6-3-6-4: 2/0

4-4-2-6?

Summary

G-U-E-S-S: Numbers correct, wrong place/numbers correct, right place

1) 2-3-4-6: 2/1

2) 1-1-5-6: 1/0

3) 6-3-6-4: 2/0

4) 4-4-2-6: 2/0

3241

Summary

G-U-E-S-S: Numbers correct, wrong place/numbers correct, right place

1) 2-3-4-6: 2/1

2) 1-1-5-6: 1/0

3) 6-3-6-4: 2/0

4) 4-4-2-6: 2/0

5) 3-2-4-1: 1/2

3-5-4-2?

Summary

G-U-E-S-S: Numbers correct, wrong place/numbers correct, right place

1) 2-3-4-6: 2/1

2) 1-1-5-6: 1/0

3) 6-3-6-4: 2/0

4) 4-4-2-6: 2/0

5) 3-2-4-1: 1/2

6) 3-5-4-2: 3/1

5-2-4-3!

CORRECT!!!!! CONGRATS!!!!

Ok, who is making the code for the next game?

ok wait.

it's gotta be 3-2-4 something.

I guess 3-2-4-2

damn

Right I have a code. Guess away! :D

First guess 1234

Summary

G-U-E-S-S: Numbers correct, wrong place/numbers correct, right place

1) 1-2-3-4: 0/2

Second guess 1-6-5-4

Summary

G-U-E-S-S: Numbers correct, wrong place/numbers correct, right place

1) 1-2-3-4: 0/2

2) 1-6-5-4: 0/3

1-0-5-4

I don't think 0 is an option.

1-5-5-4

Oh yeah, 6 sided die and all that.

Summary

G-U-E-S-S: Numbers correct, wrong place/numbers correct, right place

1) 1-2-3-4: 0/2

2) 1-6-5-4: 0/3

3) 1-5-5-4: 0/2

I guess 1-6-1-4, 1,4 or 6 needs to be repeated

Summary

G-U-E-S-S: Numbers correct, wrong place/numbers correct, right place

1) 1-2-3-4: 0/2

2) 1-6-5-4: 0/3

3) 1-5-5-4: 0/2

4) 1-6-1-4: 0/3

1-6-4-4

1-6-7-4

9-J-*-ü

Summary

G-U-E-S-S: Numbers correct, wrong place/numbers correct, right place

1) 1-2-3-4: 0/2

2) 1-6-5-4: 0/3

3) 1-5-5-4: 0/2

4) 1-6-1-4: 0/3

5) 1-6-4-4: 0/3

6) 1-6-7-4: 0/3

7) 9-J-*-ü: 0/0

1-6-6-4

Squiggle gets the nut! :D

Woohoo! Ok, who is making the next code?

I got one

6-5-4-3

Summary

G-U-E-S-S: Numbers correct, wrong place/numbers correct, right place

1) 6-5-4-3: 1/1

To divert slightly, is the 'first best five guesses' in a d6 mastermind game going to be

1111,2222,3333,4444,5555

because then you'll know the exact mix of the string, possibly with less than five guesses? or is there a 'better five' to start the guesses with?

Humble-Knight's game gets a guess too (guess two)

1,5,6,2

I don't think so, but it'll be close. Hmmm... I have to go and do some analysis, be right back.

I would think you could do a little better. For example:

First guess: 1-1-1-1 = 1/0

You know exactly one of them is a 1. You'll never have four 2s. You could carry one of the 1s over to see if you can get a correct placement.

Second guess: 1-2-2-2 = 2/0 (the 1 is in the correct place and there is one 2; next guess is 1-2-3-3)

or

Second guess: 1-2-2-2 = 0/1 (the 1 is in the wrong place and there are no 2s; next guess is 3-1-3-3)

This would get you some more information about placement and still give you the quantity information you were originally getting.

I always lead 1111 and then try a variation on the above - i there is one 1, my next guess would be 1222. I know there can't be four 2's and you can get a lot of position information from that guess: 

1. One right, wrong position: 1 is not first, no 2's
2. One right, right position: 1 is first, no 2's
3. Two right, wrong position: there is one 2 in first position and the 1 is elsewhere
4. Two right, right positions: the 1 is  in first position, one 2 elsewhere
5. etc.

Summary

G-U-E-S-S: Numbers correct, wrong place/numbers correct, right place

1) 6-5-4-3: 1/1

2) 1-5-6-2: 1/1

And we were talking about the whole guess solely 4 of some thing when I was explaining this game to some friends yesterday

1-6-4-4

I don't think the '1111,2222,3333...' plan is optimal, in terms of pure efficiency. From a bunch of spreadsheeting, I think you should always be able to get it within six guesses (though I haven't run all the possibilities), which 1111 doesn't guarantee. That said, 1111 is a lot easier to do without the spreadsheets...

Summary

G-U-E-S-S: Numbers correct, wrong place/numbers correct, right place

1) 6-5-4-3: 1/1

2) 1-5-6-2: 1/1

3) 1-6-4-4: 1/2

And using spreadsheets for this seems a little over the top

1-4-4-5

Matchstickman's comment made me wonder, and then I had to start making spreadsheets... Not using for the game, and I've stopped on them now, it was just something I needed to do.

Summary

G-U-E-S-S: Numbers correct, wrong place/numbers correct, right place

1) 6-5-4-3: 1/1

2) 1-5-6-2: 1/1

3) 1-6-4-4: 1/2

4) 1-4-4-5: 1/1

Oh, I got you. I thought you programmed an algorithm for solving these. My friend said he wanted to write one that would run the game for him

1-1-4-6?

Summary

G-U-E-S-S: Numbers correct, wrong place/numbers correct, right place

1) 6-5-4-3: 1/1

2) 1-5-6-2: 1/1

3) 1-6-4-4: 1/2

4) 1-4-4-5: 1/1

5) 1-1-4-6: 1/1

4-6-4-2!

That is correct.

I just ran it with the 1-1-1-1, 1-2-2-2, 1-2-3-3... Method and the correct answer pops up on the sixth guess that was as well