This is a numerical logical reasoning problem, and the key to solving the problem is to sort out the information of each guess, and gradually eliminate and determine the number.
It is known that the teacher wrote four non-repeating numbers, and Xiao Ming's feedback from four guesses is as follows:
1st "0529": 0, 5, 2, 9 are excluded → no correct numbers.
The second "1438": 2 numbers are guessed correctly but in the wrong position→ the correct number is in 1, 4, 3, 8 and is not in the corresponding position (1≠ thousand, 4≠100, 3≠ ten, 8≠ single digit).
The third "6187": guess 2 numbers correctly but in the wrong position→ the correct number is in 6, 1, 8, 7 and is not in the corresponding position (6≠ thousand, 1≠100, 8≠ ten, 7≠ single digit).
The fourth 6378: guess 3 numbers correctly, 2 position pairs→ combine the first three times to filter valid information.
Reasoning core
Lock the repeated numbers: the second and third times both contain "8", and the fourth time also has "8", combined with the first elimination, it is determined that "8" is the correct number, and because the second and third "8" are in the wrong position, "8" is not in the single digit or ten digits, but can only be in the thousand or hundred digits.
Analysis of the fourth guess: "6378" contains the digits 6, 3, 7, 8, combined with the previous three eliminations, the correct digits are 3, 7, 8 (including "8") and the unexcluded 6. Since "6378" correctly guesses 3 and 2 position pairs, assuming that "3" is in the 100 position (position pair) and "7" is in the 10th position (position pair), "2 position pairs" are satisfied; The remaining digits "6" and "8" need to match the thousand digits and the single digits.
Determine the final position: "6" is not in the thousand position (the third position is wrong), so "6" is in the unit position, "8" is not in the unit position, the tenth place (the second and third positions are wrong), and the "3" and "7" positions are determined, so "8" is in the thousand place.
In summary, the four-digit number is 8376 (verified, meets all the conditions for guess feedback).
