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Problem 11: THE LOCKSMITH'S CIRCLE.
A two-button keypad opens when the last n presses match the code.
A shortest cyclic sequence of 2^n presses tries every code once.
How many exist, up to rotation?
Solution 9 is live.
#QEDEventually #deBruijn #BESTTheorem #Combinatorics

Problem 10: THE WARDEN'S LOCKERS.
2n prisoners, 2n lockers, n openings each.
Open the locker with your own number, then follow the numbers you find.
What is the chance all succeed, and its limit as n grows?
Solution 8 is live.
#QEDEventually #Probability #Permutations

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