Counting puzzle from the first US puzzle championship

My students had fun with this one today. Part d is what showed up in the actual championship.

One night, in an attempt to combat insomnia, you begin counting (1, 2, 3, …), but you decide to do it digit by digit. As you go along, for example, the 15th digit you count is the 2 of the number 12.
1 2 3 4 5 6 7 8 9 10 11 12

a.) What’s the 50th digit you count?
b.) What’s the 100th digit you count?
c.) What’s the 1000th digit you count?
d.) What’s the 1,000,000th digit you count?

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