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Chalk it Out

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Your teacher has a total of 36 chalks. When a chalk reduces to 1/6 of its original size, it gets too small for her to hold for writing and hence she keeps it aside. But your teacher hates wasting things and so, when she realizes that she has enough of these small pieces to join and make another chalk of the same size, she joins them and uses the new chalkstick. If she uses one chalk each day, how many days would the 36 chalks last?
 
Hint      
  puzzle : image for chalks  


 
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