My problem with 99994 is that they may correctly deduce that that was the highest sum of digits we could reach, whereas 44444 doesn't really give any deductions and it's highly unlikely for the tiebreaker to come into play.
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For our guessing, the strategy I've come up with is:
First guess; +1 to all digits
(For example, if we receive 37966 guess 48077)
Then -1 to all digits
+2 to all digits
-2 to a digits
+0 to all digits
+3 to all digits
+4 to all digits
+5 to all digits
Because we know that the differences must sum to 15 we may be able to skip one or more of those. What this does is gets us to at most 120 combinations left after at most 8 guesses, because we will know the amount slots need to change by, we just need to arrange these changes in the correct order.
Suppose our changes our A, B, C, D, and E; Our next guess would apply them in order ABCDE
If we have 5 match we're done (9 total).
4 match is impossible.
If we have 3 match it takes at most an additional 5 guesses (14 total)
If we get 2 match it takes at most an additional 6 or 8 (idk which) guesses (15 or 17 total)
If we get 1 match it at most an additional 8 guesses. (17 total)
If we get 0 matches we than submit BCDEA and go to that many matches (18 total)
Which means unless I messed up the numbers or misunderstood something it will take at most 18 guesses.
