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:
- One right, wrong position: 1 is not first, no 2's
- One right, right position: 1 is first, no 2's
- Two right, wrong position: there is one 2 in first position and the 1 is elsewhere
- Two right, right positions: the 1 is in first position, one 2 elsewhere
- 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