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Hints:
3548 - 2 correct digits, but only 1 in the right place
4860 - 1 correct digit, but in the wrong place
2356 - 3 correct digits, but only 1 in the right place
2584 - 2 correct digits and in their place

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  • $\begingroup$ Welcome to Puzzling! Could you add the source of the puzzle? $\endgroup$ – Ak. May 18 at 13:02
  • $\begingroup$ Hello Ak, found it on internet and tried to get the result. it was on a FB page :) $\endgroup$ – Giorgian Ciocodeica May 18 at 13:06
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    $\begingroup$ Could you provide a link to/the name of the FB page? $\endgroup$ – bobble May 18 at 13:51
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Hints: 3548 - 2 correct digits, but only 1 in the right place 4860 - 1 correct digit, but in the wrong place 2356 - 3 correct digits, but only 1 in the right place 2584 - 2 correct digits and in their place

I like to tackle these by picking a starting assumption and running with it. 5 shows up in position 2 in top and bottom, so let’s start by assuming the number is _ 5 _ _. This means that only one of 2, 8, 4 is also in the right place (from 2584), and additionally only one of 3, 4, 8 are in the number but in the wrong place (from 3548). If 2 is in its correct place, then 8 and 4 are not in the number. This means that 3 is in the number. From 2356, it would follow that 2 is the correct digit in the correct place, and 3,5 are the digits in the wrong place. So our assumptions take us to 2 5 _ _ with a 3 in the last two numbers. Further, from 2356 if 2,3,5 are correct digits, then 6 is not in the number. From before, 4,8 are also not in the number, so using 4860, the 0 must be the correct digit in the wrong place. Since there are only 2 places left, the 0 must be the 3rd digit, and the 3 must be the last digit.

One possible number is therefore

2503.

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By logical deduction without guessing:

From clues 1 and 2:

4 and 8 can't be the 2 correct digits from 3548, because 4860 only has one correct. So for 3548 either (i) 3 and 5 are both correct, or (ii) one from 3/5 and one from 4/8.

Clue 3:

Taking option (ii) from above, if only 1 of 3/5 is correct, then 2 and 6 are the other two correct digits from 2356. So we now have 2, 6, one from 3/5 and one from 4/8. But that gives us a contradiction, because that would require that two digits from 4860 are correct. So option (ii) is not possible.

So we now have:

3 and 5 are correct (clue #1). 4 and 8 are out, so one of 6/0 is correct (clue #2), and one of 2/6 is correct (clue #3).

Clue #4:

If 4 and 8 are out, then 2 and 5 must be the correct digits, so the answer is 25xx. If only one of 2/6 is correct, obviously that's now 2, so 6 is out leaving 0 as the correct digit from clue 2. Since that's in the wrong place there, then the answer is 250x, and we already know three is correct, so the answer is 2503.

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Frequency approach

The numbers 0-9 have frequency 1,0,2,2,3,3,2,0,3,0
Those can add to up to the number of correct digits (8) in only 2 ways
3+3+2+0 or 3+2+2+1

Option 1 requires 2 of the numbers 4,5,8. With this:
the 1st guess excludes 3
the 4th guess excludes 2
the 3rd guess needsat least on one of those -> contradiction

Option 2 requires 0 (the only one with frequency 1).
With this guess 2 excludes 4,6 and 8, which means (due to guess 3) that 2,3,5 are needed
with the numbers known:
guess 4 gives the position of 2 and 3 and then guess 2 the position of 0
-> (only) solution: 2503

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The same answer as El-Guest, but with a different approach:

Consider the second assumption. if 4 is the correct digit, then 6 can't appear in the solution. The third assumption would then prove that 2,3 and 5 are all correct digits, making the solution a permutation of 2345. However, the first assumption would then be false. Hence 4 is not a correct digit.

Exactly the same reasonning proves that:

8 is not a correct digit either.

As a consequence

The correct digits is the fourth assumption are 2 and 5. From there, direct deductions show that 3 is part of the solution (from first assumption), that 6 isn't (third assumption), that 0 is a correct digit and that it stand in third position (second assumption).

Finally, the unique solution is:

2503

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Another way:

If 6 in 2356 is correct, then either of 2, 3, 5 must be wrong (since 2356 has only 3 correct digits). But (from 3548 and 2584) we can say that either 4 or 8 should be correct (since at least one of the "35" and "25" groups contains a wrong digit, so to get 2 correct digits in 2584 and 3548, one of the 4 and 8 should be correct). But we get a contradiction since 4860 now contains 2 correct digits (6 and at least one of 4 and 8).
So, 6 is wrong, and 2, 3, 5 are all correct. Now we can say that 4 and 8 are wrong, since we already reached the limit of right digits in 2548/3584. So, 0 is correct since it is the only remaining "unknown" digit of 4860.
From 2584, 2 and 5 are in the right places (we now have 25xx), 0 is in the wrong place from 4860 (we have 250x - only remaining place for the 0), and the last place should be occupied by the 3 (the final correct digit). So, the final answer is 2503.

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