Errorless, invisible, continuous and infrastructure-free healthcare should become our goal. In order to achieve that goal, we need to rapidly move from current episodic and emergency-driven “healthcare delivery system” to an intelligent and extelligent health environment. That requires introduction of distributed affective Intelligent Caring Creatures (ICCs) consisting of healthons. Healthons are tools combining prevention with diagnosis and treatment based on continuous monitoring and analyzing of vital signs and biochemistry. Unlike humans, who posses only two or three dimensions of thinking, healthons can assure errorless health because of their adaptability, flexibility, and multidimensional reasoning capability. ICCs can do “the right thing” based on (1) state-of-art medical knowledge, (2) data about emotional, physiological, and genetic state of a consumer and (3) moral values of a consumer. The transition to the intelligent health environment based on ICCs requires the solutions to many currently unsolved healthcare problems. This paper lists the unsolved problems (by analogy to mathematical unsolved problems list) and explains why errorless healthcare with bionic hugs and no need for quality control is possible.