Bulls and Cows

Thread Games
81

Interesting choice. 0864 has no bulls and one cow.

# guess Bulls Cows
1 0864 0 1
82

Next, 5321.

83

5321 has one bull and one cow.

# guess Bulls Cows
1 0864 0 1
2 5321 1 1
84

7986, so that we can see how we stand.

85

7986 has no bulls and one cow.

# guess Bulls Cows
1 0864 0 1
2 5321 1 1
3 7986 0 1
86
  1. :slight_smile:
87

4790 has two bulls and no cows.

# guess Bulls Cows
1 0864 0 1
2 5321 1 1
3 7986 0 1
4 4790 2 0
88
89

8 and 6 are not included in the secret number because the fourth digit is either 7 or 9 and the number that includes both 7 and 9 has produced only 1 cow (all the other three digits being included in the two previous numbers, that is 0864 and 5321).

Point A. We can say the first digit we know in the secret number is either 7 or 9 (because 8 and 6 are not included in the secret number).
Point B. We can say the second digit we know in the secret number is either 0 or 4 (because 8 and 6 are not included in the secret number).
Point C. The third and fourth digits two of the four included in the second number I guessed: 5321.

Prof.Pepeerwinkle’s number may produce 2 bulls if 5 is the bull in the second number I guessed and if the second digit I mentioned in Point B is 0, (and 0’s position is not the third or fourth place in the secret number).

The remaining matches that Prof.Pepperwinkle’s number can produce are 1 bull and 1 cow, 2 cows, or 1 cow (for reasons that I won’t elaborate).

Prof.Pepperwinkle’s number will not produce 3 bulls, 4 bulls, or 0 bulls & 0 cows.

90

5064 has no bulls and one cow.

# guess Bulls Cows
1 0864 0 1
2 5321 1 1
3 7986 0 1
4 4790 2 0
5 5064 0 1
91

Let’s try 4723.

92

4723 has no bulls and two cows.

# guess Bulls Cows
1 0864 0 1
2 5321 1 1
3 7986 0 1
4 4790 2 0
5 5064 0 1
6 4723 0 2
93

3590?

94

Getting closer. 3590 has two bulls and one cow.

# guess Bulls Cows
1 0864 0 1
2 5321 1 1
3 7986 0 1
4 4790 2 0
5 5064 0 1
6 4723 0 2
7 3590 2 1
95

If my calculations are right, there is enough information already presented to narrow the choice down to one.

96

I don’t doubt your calculations are right.

It is a pity the game doesn’t attract more players. There are few views and much fewer participants.

97

Yep. And thanks for starting this thread; I’m finding it absolutely fascinating.

98

2390?

99

Ding-ding-ding-ding! We have a winner. Congratulations, Aspidistra. Now you’re the game master for the next round.

# guess Bulls Cows
1 0864 0 1
2 5321 1 1
3 7986 0 1
4 4790 2 0
5 5064 0 1
6 4723 0 2
7 3590 2 1
8 2390 4 0
100

Congratulations @Aspidistra !