Neat Fact:

Every integer greater than 8 has at least two letters in common with each of its neighbours (source).

Neat Trick:

When the magician leaves the room, the trickees lay out eight coins in a row deciding which side is turned up according to their whim. They also think of a number between 1 and 8 inclusive. The magician’s assistant then flips exactly one of the coins, before inviting the magician back in. The magician looks at the coins and guesses the number that the trickees thought of.

Neat Puzzle:

“Last semester I offered my students $1,000,000 dollars. They

turned me down. This was lucky, despite the money and glamour of

academic mathematics, I do not have a million dollars. The game was

simple. The class of 100 each had to write a number. The highest number

won. Of course there was a catch, the prize was $1,000,000 divided by

the winning number. The best outcome for the students as a whole would

come if everyone wrote 1, $10,000 is not a bad return for a lecture. Of

course if everyone is writing 1, the person who writes 2 wins and makes

far more for themselves. What happened?” (Source)

BEPOK, now explain that “trick”.