Problem 185
Number Mind
The game Number Mind is a variant of the well known game Master Mind.
Instead of coloured pegs, you have to guess a secret sequence of digits. After each guess you’re only told in how many places you’ve guessed the correct digit. So, if the sequence was 1234 and you guessed 2036, you’d be told that you have one correct digit; however, you would NOT be told that you also have another digit in the wrong place.
For instance, given the following guesses for a 5-digit secret sequence,
90342 ;2 correct
70794 ;0 correct
39458 ;2 correct
34109 ;1 correct
51545 ;2 correct
12531 ;1 correct
The correct sequence 39542 is unique.
Based on the following guesses,
5616185650518293 ;2 correct
3847439647293047 ;1 correct
5855462940810587 ;3 correct
9742855507068353 ;3 correct
4296849643607543 ;3 correct
3174248439465858 ;1 correct
4513559094146117 ;2 correct
7890971548908067 ;3 correct
8157356344118483 ;1 correct
2615250744386899 ;2 correct
8690095851526254 ;3 correct
6375711915077050 ;1 correct
6913859173121360 ;1 correct
6442889055042768 ;2 correct
2321386104303845 ;0 correct
2326509471271448 ;2 correct
5251583379644322 ;2 correct
1748270476758276 ;3 correct
4895722652190306 ;1 correct
3041631117224635 ;3 correct
1841236454324589 ;3 correct
2659862637316867 ;2 correct
Find the unique 16-digit secret sequence.
数字头脑
“数字头脑”游戏是著名的游戏“大师头脑”的一个变种。
在“数字头脑”中，你需要猜测一个数字序列，而不是“大师头脑”中的彩色方块。每次猜测之后，你会被告知你猜对了多少个位置上的数字。因此，如果正确的序列是1234，而你猜的是2036，那么你会被告知你猜对了一个位置上的数字。然而，你并不会知道你是否猜对了数字但不在其正确位置上。
例如，根据你对一个五位的数字序列作的如下猜测：
90342；2个数字正确
70794；0个数字正确
39458；2个数字正确
34109；1个数字正确
51545；2个数字正确
12531；1个数字正确
唯一正确的序列是39542。
根据下面的猜测，
5616185650518293；2个数字正确
3847439647293047；1个数字正确
5855462940810587；3个数字正确
9742855507068353；3个数字正确
4296849643607543；3个数字正确
3174248439465858；1个数字正确
4513559094146117；2个数字正确
7890971548908067；3个数字正确
8157356344118483；1个数字正确
2615250744386899；2个数字正确
8690095851526254；3个数字正确
6375711915077050；1个数字正确
6913859173121360；1个数字正确
6442889055042768；2个数字正确
2321386104303845；0个数字正确
2326509471271448；2个数字正确
5251583379644322；2个数字正确
1748270476758276；3个数字正确
4895722652190306；1个数字正确
3041631117224635；3个数字正确
1841236454324589；3个数字正确
2659862637316867；2个数字正确
求出唯一正确的16位序列。