Can a Schizophrenic do it ?

Can a Schizophrenic give unimaginable correct solution ? I was seeing a movie in which a joke scine took me about 30 years back. I was working in Govt mental hospital where about 2000 patients were admitted more than its capacity. A chronic, regressed, Schizophrenic used to wander whole day in the campus, collecting things from the road, always muttering, careless & looking like a street begger. He always remained indifferent. On that morning we all were very worried as someone has taken out all the four nuts of a wheel of the hospital's truck which has to carry grains for the patients. I was tense I noticed Debu (patient) going, to relax myself I called him and asked the solution, he was continuing his muttering, he said in a very low voice " take out one nut from each wheel" and went away. Now when I am seeing a movie the question hammers me that can a Schizophrenic of this stage (he was in the hospital for last 10 years) give such an intelligent answer ?

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Dr John Forbes Nash, American Mathematician and Nobel Laureate , was a full blown Schizophrenic, with hallucinations. He was a professor in his speciality. " A Beautiful Mind " , Hollywood film, is all about his turmoil and triumphs.

Schizophrenic can be very intelligent, sharp and they can give correct advice on many circumstances

Thank you doctor
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If patient is chronic with negative symptoms, regressed then d skills gets affected. I was in CIP KANKE Ranchi. Very renowned mathametician dr Vashisht Narain Sinha was admitted in RHC, was not able to count nos. There was profound deterioration found in him.