First, divide 1 boys and 2 girls 14 children into one group, so that 17 people just move 17 bricks, with an average of 1 brick per person.

100/ 17 = 5 (group). 15 (person), (block)

That is to say, it can be divided into five groups, but there are still 15 people missing, leaving 15 bricks.

Then divide 1 woman and 4 children into a group, so that 5 people can move just 5 bricks, which is 1 brick per person.

15/5 = 3 (group)

So you can get a group of five men, 5 * 2+3 = 13 women, 5 * 14+3 * 4 = 82 children.

Another equation method is provided:

Suppose there are x men and y women, then there are (100-x-y) children. Do the equation:

4X+3Y+( 100-X-Y)/2 = 100

Deformation: y = 20-7x/5

Because the number of people must be an integer and 5 and 7 are prime, X must be a multiple of 5.

When x = 5, y = 13, 100-5- 13 = 82.

When x = 10, y = 6, 100- 10-6 = 84.

If men, women and children must have it, there are only two sets of solutions.