## Number Mind

### Problem 185

Published on Saturday, 8th March 2008, 01:00 am; Solved by 1960; Difficulty rating: 55%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.