79978
56789 - 3 correct, 2 in place
there are 10 possible correct configurations.
56xxx - accounts for a change of 5 from the shuffled position.
5x7xx - accounts for a change of 4 from the shuffled position.
5xx8x - accounts for a change of 3 from the shuffled position.
5xxx9 - accounts for a change of 3 from the shuffled position.
x67xx - accounts for a change of 5 from the shuffled position.
x6x8x - accounts for a change of 4 from the shuffled position.
x6xx9 - accounts for a change of 4 from the shuffled position.
xx78x - accounts for a change of 3 from the shuffled position.
xx7x9 - accounts for a change of 3 from the shuffled position.
xxx89 - accounts for a change of 2 from the shuffled position.
We know one of 01234 is correct, but none in the right position. Additionally, we know something is repeated, but not which number.
so a max of 5 changes is possible from that number within 0-4.
So we know at least 5 changes come from the last 2 digits we don’t know anything about. We know it’s another number between 5-9 so we can keep adding onto the possibilities:
56xxx - First
568xx - one additional.
569xx - IMPOSSIBLE.
56x7x - IMPOSSIBLE.
56x9x - two additional.
56xx7 - one additional.
56xx8 - IMPOSSIBLE.
I can keep going from here and write out all possible answers to establish what our next guess should be but I kind of want more eyes on this. Does this seem worth it?
