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  2. Collatz conjecture - Wikipedia

    en.wikipedia.org/wiki/Collatz_conjecture

    For instance, the first counterexample must be odd because f(2n) = n, smaller than 2n; and it must be 3 mod 4 because f 2 (4n + 1) = 3n + 1, smaller than 4n + 1. For each starting value a which is not a counterexample to the Collatz conjecture, there is a k for which such an inequality holds, so checking the Collatz conjecture for one starting ...

  3. Doctors Say This Viral "Sleep Rule" Actually Works - AOL

    www.aol.com/lifestyle/doctors-viral-sleep-rule...

    How to follow the 10-3-2-1-0 sleep rule 10 hours before bed: No more caffeine. ... Shop the best under-$50 clothing items to grab right now on Amazon. AOL.

  4. I Wanna Run Barefoot Through Your Hair - Wikipedia

    en.wikipedia.org/wiki/I_Wanna_Run_Barefoot...

    Reviewing the album for AllMusic, Fred Thomas awarded it a four and a half out of five star rating and wrote that, "I Wanna Run Barefoot Through Your Hair highlights how Owens can write songs detailing life's harshest miseries and somehow twist them until the main takeaways are hope and gratitude. It's a rare feat, and Owens accomplishes it on ...

  5. Monty Hall problem - Wikipedia

    en.wikipedia.org/wiki/Monty_Hall_problem

    With his strategy, the player has a win-chance of at least ⁠ 2 / 3 ⁠, however the TV station plays; with the TV station's strategy, the TV station will lose with probability at most ⁠ 2 / 3 ⁠, however the player plays. The fact that these two strategies match (at least ⁠ 2 / 3 ⁠, at most ⁠ 2 / 3 ⁠) proves that they form the ...

  6. Inside the fight against the counterfeit goods market, and ...

    www.aol.com/inside-fight-against-counterfeit...

    The Customs and Border Protection agency, which is in part responsible for enforcing intellectual property rights and upholding trade laws, seized $3.33 billion worth of counterfeit goods in 2021 ...

  7. Discover the best free online games at AOL.com - Play board, card, casino, puzzle and many more online games while chatting with others in real-time.

  8. 10+2 (TV series) - Wikipedia

    en.wikipedia.org/wiki/10+2_(TV_series)

    10+2 is a children's animated series from Catalonia (Spain), produced by Accio Studios and Victory Media Group, and directed by Miquel Pujol i Lozano. The show debuted in 1991. The show debuted in 1991.

  9. The worst offender of this Silent Princess Syndrome is "Aladdin," in which Jasmine speaks only 10 percent of the movie's lines. In the midst of Disney's commercially and critically successful renderings of fairy tales, women authors were working away behind the scenes to whip up their own bold takes.