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C00002 00002	(1) Let  S[i] = abb...bcdd...d...eff...f, where  a,b,c,d,...e,f  are strings
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(1) Let  S[i] = abb...bcdd...d...eff...f, where  a,b,c,d,...e,f  are strings
of decimal digits and  b,d,...,f  are repeated  i  times,  a  contains a
non-zero digit, and  bd...f  is not the empty string.  Show there are
infinitely many  i  for which  S[i]  is not the decimal representation of a
prime number.

(2) A magazine with 100,000 subscribers announces that those requesting
free renewals will get them, provided not more than 20 percent so request.
Assume all subscribers are rational.  What is the best policy for a subscriber?

(3) A radio station offers a prize to the tenth caller in the next hour.
There are known to be one hundred listeners.  Callers are restricted to
one call.  Equipment can handle any number of overlapping calls.  Exactly
simultaneous calls are disqualified.  Assuming rationality of all listeners,
and impossibility of collusion or spying, what is a listener's best strategy?

(4) Let  X  be a finite set of cardinality  n.  How many functions from
X  to  X  are required so that, by composition, one can form all the functions
from  X  to  X?