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Four problems

(1) Let $S↓i=ab↑icd↑i\ldots ef↑i$, where $a,b,\ldots ,f$ are strings of
decimal digits, $a$ begins with a non-zero digit, and $bd\ldots f$ is
not the empty string.  Show the sequence $S↓i$ contains infinitely many
nonprimes.

(2) I roll a die 600 times.  Which is the greater: the probability of
rolling more than 100 sixes, or the probability of less than 100 sixes?
By about how much?

(3) 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?

(4) 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?