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quizzes, puzzles and tricks

Sequence

Replace the ‘X’ in the following sequence with the most appropriate number:

1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 7, 4, 8, 1, 9, 5, 10, 3, 11, 6, 12, 2, 13, 7, 14, 4, 15, 8, 16, 1, 17, 9, 18, 5, 19, 10, 20, 3, 21, 11, 22, X, …

Answer at 10 p.m. this evening, as usual.

[H/T G. Sarcone]…

Which country …

… has this associated with it? [Five separate countries]:

1. For one day in 1943, the capital city designated a hospital room to be “extraterritorial” (international) ground so a Dutch princess could be born a full Dutch citizen.

2. It’s an archipelago made up of over 100 islands, some of which are not even inhabited but the inhabited ones have 14 Nobel Laureates altogether.…

The 1000 lockers

A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:

There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it.

Then he has the second student go to every second locker and close it.

The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it.

The fourth student does this to every fourth locker, and so on.

After the process is completed with the thousandth student, how many lockers are open?…