It is known each next number in the sequence has at least one digit in common with the previous one.
What is the second digit in the three-digit number which should be placed instead of the question mark?
The difference between the two neighboring numbers decreases by 1 with each next couple:
348-242=106
453-348=105
557-453=104
Thus, the last number should be 103 bigger than 557, i.e. 660. But it is known this number should have at least one digit in common with 557. In fact the numbers in the sequence are digital clock times. Thus, 557 should be considered as 5:57. The time 103 minutes bigger is 7:00 having the “7” in common with 5:57. Thus, the second digit in the last number is 0.