Problem: Matthew says that Christ healed two men, but Mark refers to only one man being healed (10:46). This appears to be a clear contradiction.
Solution: Although Mark records one individual getting healed, this does not mean that there were not two, as Matthew says there were. First of all, Mark does not declare that there was only one blind man healed. Matthew says there were two, and where there are two there is always one, every time! Matthew earlier mentions two demoniacs where Mark and Luke mention one (Matt. 8:28–34), so Matthew again mentions the two blind men where Mark mentions just one. Further, the fact that Mark mentions the name of one blind man, Bartimaeus, and his father (Timaeus, 10:46), indicates that Mark is centering on the one that was personally known to him. If two men were to receive a medal of honor from the president of the United States and one was your friend, it is understandable that when you relate the story you might only speak of the one whom you knew receiving the medal.