Comments by "" (@mina86) on "Mathologer" channel.

  1. I did it by walking from left to right and recursive application of two lemmas: Lemma 1: There’s odd number of doors between blue and green points. Lemma 2: There’s even number of doors between green and green points. Proof of Lemma 1: We start at a blue point. The next point is either 1) blue in which case the problem is reduced back to L1; or 2) green in which case there’s a door and based on L2 additional even number of doors for a total of odd number of doors. Proof of Lemma 2: We start at a green point. If that’s the end, there’s zero (even) number of doors. Otherwise, the next point is either 1) green in which case the problem is reduced back to L2; or 2) blue in which case there’s a door and based on L1 additional odd number of doors for a total of even number of doors. Now, from Lemma 1, there’s odd number of doors between blue point on far left and green point on far right. ∎
    4
  2. I’ll take a wild guess that you haven’t watched the videos yet.
    2
  3. Consider that the room might be closer to the coffee shop downstairs, and thus better WiFi signal. ;)
    2
  4. There actually isn’t only one special room that leaves the house. But yes, now you just need to prove that there is an odd number of special rooms leaving the house.
    1
  5. Simple, … = 71/12.
    1