Question 1159949
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In my view, this problem, as worded and formulated, is defective.


Indeed, it says "every time when . . . ", but does not specify what is the time interval between two adjacent events.


So, it is not possible to answer literally "how long it will take".


We only can answer, after how many discrete time intervals it will happen, but the duration 
of a real "elementary" time interval remains unknown.


Any Physicist will see this deficiency MOMENTARILY . . . 



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Surely, I found the links in the Internet to the PRECISELY CORRECT formulation of this problem


https://books.google.com/books?id=zYBi6cxYCVkC&pg=PA60&lpg=PA60&dq=Every+time+the+mouse+starts+nibbling+at+the+hunk+of+cheese,+the+cat+takes+advantage&source=bl&ots=4j2i8imMve&sig=ACfU3U3m-TC0SSztsn6eRARM6U7NPFtyfw&hl=en&sa=X&ved=2ahUKEwiUltzA6c_pAhUIqZ4KHaQoD28Q6AEwAHoECAkQAQ#v=onepage&q=Every%20time%20the%20mouse%20starts%20nibbling%20at%20the%20hunk%20of%20cheese%2C%20the%20cat%20takes%20advantage&f=false


and


https://books.google.com/books?id=zYBi6cxYCVkC&pg=PA60&lpg=PA60&dq=Every+time+the+mouse+starts+nibbling+at+the+hunk+of+cheese,+the+cat+takes+advantage&source=bl&ots=4j2i8imOxg&sig=ACfU3U0STbrKsQ6C1Qs-q7eyCkHuVWmgNA&hl=en&sa=X&ved=2ahUKEwiEk9Wq6s_pAhUDOn0KHZU-AHgQ6AEwAHoECAoQAQ#v=onepage&q=Every%20time%20the%20mouse%20starts%20nibbling%20at%20the%20hunk%20of%20cheese%2C%20the%20cat%20takes%20advantage&f=false



I hate it very much when people bring  "dirty"  formulated problems to the forum.