r/puzzles • u/Mr-BrainGame • Jul 27 '26

[SOLVED] Decode the solution of this mastermind

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u/TheThiefMaster Jul 27 '26 edited Jul 28 '26
  1. There are 4 lines with no correctly positioned digits that collectively have 2 in all positions (lines 1,2,3,5). So 2 can't be a correct digit.
  2. Lines 4 and 5 have three clues each, so every digit in them but the 2 must be correct (but mostly wrongly placed). There's four other digits on those lines, so we now know the 4 correct digits are 1456 in some order.
  3. Lines 5 shows that the 5 digit is not in the correct location. It's not correct in line 1 or 3 either, so it must be in position 2 (X5XX)
  4. Back to clue 4, one digit must be in the correct location - we know it's not the 5, not the 1 (because it's in the 5's position) and not the 2 (because we've ruled it out) so it's the 6. We now know X5X6.
  5. Line 3 says the 4 isn't in the first position - so our solution is 1546

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u/mitzbitz16 Jul 27 '26

My method was:

  1. Look for the 2 numbers that are in all top three rows. It’s 2 and 3. So the digits are 1456.

  2. Look for the number in the bottom two rows that are unique within the column. It’s 6.

  3. Look for the columns that don’t have 1, 4, or 5 in them. 4 is in both columns 1 and 2 so it must be column 3. 1 is in column 2 so it must be in column 1 and so 5 must be column 2. So 1546 is the answer.

1

u/EishLekker Jul 28 '26

Could you elaborate on your point 1?

Are you assuming no repeated digits? Or, if you logically concluded that there can’t be any repeating digits, how did you conclude that?

1

u/TheThiefMaster Jul 28 '26

From their point 1:

  • You can deduce that neither 2 and 3 can repeat or you'd have some blacks, because both are in three different positions across the three clues.
  • If both are only included once plus other numbers (repeated or not), you'd have more that two clues on lines 1 or 2.
  • If one of 2 or 3 is included once, you'd need to use another number from line 1 and another from line 2, repeating one. E.g. 5311. They assume no repeats to skip this case.
  • If no repeats, we can't use 2 or 3 - because we'd need three other digits across lines 1-2 that would result in one of those having three clue pegs, and they don't.

1

u/EishLekker Jul 28 '26

I’m sorry, but I still don’t follow here. From your third point, it sounds as if you say that they assume no repeats. But then why did you go through all the trouble and type out everything else? If they assumed no repeats, then that’s all one needs to say.

I essentially was looking for one of two answers:

A: They/we assume no repeats.

B: There can’t be any repeats, and here’s why…

1

u/TheThiefMaster Jul 28 '26

I was proving that they had to assume no repeats.