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Persistence I (Posted on 2017-12-24) Difficulty: 3 of 5
Let's define persistence of an integer number p(N) as the number of times one has to multiply said number's digits before reaching a single digit.
Examples: 48==>32==>6, so p(48)=2;
23568643407==>0 , so p(23568643407)=1

Three tasks:
a. (easy). Comment on the value of p(N!) for a non-negative N.
b.(harder) What can be said of the values of p(N) in bases 2 or 3.
c. (hardest) How many 3-digit integers with p(N)=3 are there?

Try to solve analytically.

See The Solution Submitted by Ady TZIDON    
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Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some Thoughtssome analysis; some computation-- solution except for b) in base 3.Charlie2017-12-24 14:13:06
The easy onesJer2017-12-24 13:52:03
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