Solution: House D. 

   

If the bus stops at house A, we will have

·         2 children walk 0 ft;

·         3 children walk 100 ft each;

·         4 children walk 200 ft each;

·         5 children walk 300 ft each;

·         6 children walk 400 ft each

Altogether, they walk 5000 ft.

If the bus stops at house B, we will have

·         3 children walk 0 ft;

·         6 children walk 100 ft each;

·         5 children walk 200 ft each;

·         6 children walk 300 ft each

Altogether, they walk 3400 ft.

If the bus stops at house C, we will have

·         4 children walk 0 ft;

·         8 children walk 100 ft each;

·         8 children walk 200 ft each;

Altogether, they walk 2400 ft.

If the bus stops at house D, we will have

·         5 children walk 0 ft;

·         10 children walk 100 ft each;

·         3 children walk 200 ft each;

·         2 children walk 300 ft each;

Altogether, they walk 2200 ft.

If the bus stops at house E, we will have

·         6 children walk 0 ft;

·         5 children walk 100 ft each;

·         4 children walk 200 ft each;

·         3 children walk 300 ft each;

·         2 children walk 200ft each.

Altogether, they walk 2600 ft.

Children walk the least if the bus stops at House D.