4. How many four-digit natural numbers greater than 7777 have the sum of their digits equal to 32? Write them down!
4. The appropriate quadruples of digits are: a) $9,9,9,5$,
b) $9,9,8,6$,
c) $9,9,7,7$,
d) $9,8,8,7$,
e) $8,8,8,8$.

The numbers with the desired properties are:
a) $9995,9959,9599$,

b) 9986, 9968, 9896, 9869, 9698, 9689, 8996, 8969, 8699,
c) $9977,9797,9779,7997,7979,7799$,

d) 9887, 9878, 9788, 8987, 8978, 8897, 8879, 8798, 8789, 7988, 7898, 7889,
e) 8888.

There are a total of 31 such numbers.