How can suitable kidney donors be found for patients in need?

Being Solved by Mathematicians

Suppose you need a kidney transplant and your brother Arnold offers to donate one of his kidneys to you. You discover that since your blood type is O his blood type is A, your body would reject his kidney.

Another patient, Sheldon, also needs a kidney. His wife Ann had hoped to donate a kidney to Sheldon, but his blood type is A and her blood type is O. Ann agrees to donate a kidney to you on the condition that your brother Arnold donates a kidney to Sheldon – and in both cases the kidneys are compatible. Especially for rare blood types, this kind of Paired Kidney Donation can save lives by matching willing, compatible kidney donors to patients in need.