Mathcounts National Sprint Round Problems And Solutions

How many 4-digit numbers have at least one digit repeated?

Problem (Mock National Level):A bag contains 5 red marbles and 5 blue marbles. If three marbles are drawn at random without replacement, what is the probability that at least two are red? Mathcounts National Sprint Round Problems And Solutions

The contestants realized that the length of the other leg, 8, was indeed a crucial piece of information. By using 8 as an exponent, they could unlock the recursive sequence: $a_n = 2a_n-1 + 3$, and ultimately find $a_4$. How many 4-digit numbers have at least one digit repeated