The assignments of students rely in large part on a random number assigned by a computer. So a system designed for fairness can inevitably cause divisions among winners and losers. 

Of the many complexities of the city’s school assignment system, it is this central inequity that can inflame the most passionate anger, that the city can pay for many but not all of its 4-year-olds to go to school.

In Boston, proximity to a school - even one just 33 child-size steps away - is no guarantee of admission. 

There was a time when all the kids on Montvale Street went to nearby Wolfgang Mozart Elementary School. Now, the children scatter every morning to schools beyond their neighborhood.

Instead of preparing for the first day of school, some parents are still battling disappointment or weighing options in August, uncertain or unsettled about where their child will go.

Almost 10,000 Boston students — nearly 18 percent of the student body — are still on waiting lists, trying to get into different schools than they were assigned. 

The uneven distribution of great facilities and programs underpins Boston’s elaborate school-lottery system, and is also the reason the process is so harrowing.

The lottery system for Boston public schools has created a group of prized schools and a group perpetually relegated to second-rung status. 

This effort marks the third attempt at an overhaul, a hot-button issue that has polarized parents, community activists, and political leaders in the past.