Let N = abcd with 3000< N < 4000
We require a < b < c < d
starting with a = 3,
a = 3, b = 4, c = 5, d = 6,7,8,9 4 numbers
---------------- c = 6, d = 7,8,9 3 numbers
---------------- c = 7, d = 8,9 2 numbers
---------------- c = 8, d = 9 1 number
total sum = 1+2+3+4 = 10
a = 3, b = 5, c = 6, d = 7,8,9 3 numbers
---------------- c = 7, d = 8,9 2 numbers
---------------- c = 8, d = 9 1 number
total sum = 1+2+3 = 6
a = 3, b = 6, c = 7, d = 8,9 2 numbers
---------------- c = 8, d = 9 1 number
total sum = 1+2 = 3
a = 3, b = 7, c = 8, d = 9 1 number
total sum = 1
Sum of totals = 1 + 3 + 6 + 10 = 20
Answer: there are 20 digit-increasing numbers between 3000 and 4000