This assumes that, during the Cuban Missile Crisis, Kennedy's advisors had managed to convince him to go with the "military option" for solving the Crisis.
That consists of:
1) Demanding the Soviets remove the missiles
2) If they refuse, use massive strikes with conventional weapons to destroy the bombs.
3) Follow that up 18 days later with an invasion.
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So, how would the situation turn out?
Would cooler heads manage to prevail, averting WW3 and making this just a more severe crisis?