The family seemed to defy the rules of genetics.

When Meriel M. McEntagart, a geneticist at St. George’s University of London, met the family in May 2012, she suspected that three of the children had a rare genetic disorder called Smith-Magenis syndrome. They had many of the symptoms of the disease, such as trouble sleeping through the night. Dr. McEntagart confirmed that diagnosis with a genetic test. The children were all missing an identical chunk of a gene known as RAI1.

One of the children had a different father from the other two, and so the mother could be the only source of their altered gene. But when Dr. McEntagart ran a standard blood test on the mother, the results were not nearly so straightforward: The woman had a normal version of RAI1.

Dr. McEntagart and her colleagues suspected that the answer to this puzzle was that the mother was a genetic mosaic.

We tend to think of ourselves as having just one set of genetic material, which exists in identical form in every one of our cells. But sometimes, people have two or more significantly different genomes. As our cells divide, some may go through a major mutation. So some individuals end up with groups of cells that have very different DNA from the rest of them.