Many parents, who are blessed with smart children, assume that the nation’s top universities are going to be equally impressed with their teenagers. And, most importantly, they assume that these institutions will be showering their children with merit scholarships.

I recently received the following email from an irate mother, who is a physician, as is her husband. The note generated 76 comments on my blog, TheCollegeSolution.com.

Here is a condensed version:

My daughter is a National Merit Finalist and president scholar nominee. She earned a 35 (out of a possible 36) on her ACT and a 2370 (out of a possible 2400) on her SAT. She is a straight ""A student with multiple Advanced Placement classes all with the highest scores of 5. She played soccer and piano. She is an artistic and academic genius with outstanding essays and teacher/counselor recommendations.

My daughter got accepted to every school to which she applied: University of Chicago, Duke, Washington University in St. Louis…to name a few.

Here’s the drum roll…No scholarship money anywhere! The schools expect us to cover 100% of the cost. My husband and I saved $168,000 for college. We were told to cover the remaining amount from our own retirement accounts!

Merit alone is not rewarded in this country. Smart financial planning and saving is penalized. She would have gone free anywhere if her parents had been dumb sloths.

What is hardest to swallow as her mother is that my taxes pay for less hardworking kids with far less merit to go to these schools for free. And these very kids love to brag about their “scholarships.”

The reaction to this mom was clearly divided. Some identified with her and felt the system should reward bright students regardless of their income. Other parents were appalled, including one mother who said, “This childish tantrum, frankly, makes me feel a little ill.”

What many families don’t understand is this: If money is an issue, teenagers have to be strategic when applying to schools. And that means knowing what kind of colleges and universities would be more inclined to give a teenager money.

The physicians’ daughter struck out because she applied to schools that are a magnet for other equally accomplished rich teenagers. There are about two dozen schools in this country that don’t award any merit scholarships to rich students. These schools include all the Ivy League members, as well as institutions like Amherst College, Massachusetts Institute of Technology, California Institute of Technology, Georgetown, Pomona, Stanford and Vassar.

These elite schools, which are all located on the coasts, don’t have to dispense merit scholarships because their brand names attract full-pay applicants who won’t be deterred by a $250,000 price tag. While rich students who get into these schools will pay full-price, these institutions represent winning an education lottery for students who need financial aid. These school typically meet 100 percent of their students’ demonstrated financial need.

Other schools high up in the rankings dispense a limited number of merit scholarships that are often quite small. At Johns Hopkins and Boston College, for instance, just 1 percent of the freshmen class received merit scholarships. Duke recently gave merit scholarships to 60 students out of a freshman class of 1,730. University of Chicago and Washington University are more typical of merit scholarships for schools with high ranks. Their average merit scholarships are in the $10,000 range and are given to 15 percent and 14 percent of their student bodies, respectively.

A friend of mine, whose child also is a National Merit Finalist, had a different experience when her child applied to schools during the latest admission season. Her son cast a wider net. He applied to schools that don’t enjoy instant cache. The family focused on schools that simply have to compete harder at attracting the most brilliant students and, frankly, most schools fall into that category. Her son applied to lesser-known liberal arts colleges featured in Colleges That Change Lives. Her son will be heading to one of those schools—Denison University—in the fall after receiving a scholarship worth $176,000.

I heard about another wealthy boy from San Diego recently whose list of acceptances this spring included Harvard and St. Olaf College in Minnesota. He received nothing from Harvard, but more than $160,000 from St. Olaf.

The vast majority of schools in this country will give bright students merit aid. But to get the best offers, you have to look beyond the elite institutions.