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Pinocchio has a magic nose, which will stretch out $5$ cm if he tells a lie and will shorten itself $1$ cm if he tells a truth. At the beginning his nose was $11$ cm long. The length of his nose changed into $13$ cm after he had said $10$ sentences. If these sentences were not true, they were definitely false. Thus, there were~\uline{~~~~~~~~~~}~truths among these $10$ sentences. 
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If these $10$ sentences are true, the nose will shorten $10$ cm. There are $(13-11+10)\div(5+1)=2$ sentences which are false. Thus, $10-2=8$ sentences are true. 