My magician gives you 3 regular dice
and asks you to do the following, while he is out of the room:
"Roll them, and write in sequence the three results, followed by a 3-digit number representing the hidden sides of the rolled dice.
Once you got the 6–digit number, divide it by 111.
THEN CALL ME."
Then he exits and you roll 1,2,4 and write down 124653, divide by 111 and get 1123.
The magician upon entering the room gets the result and quips within a second 1,2,4.
How did he do it?
You receive a strange letter stating the following:
You are one of 20 logicians worldwide to receive this letter. You don't know each other, but you all think alike. An address is given, and you are told that if a letter is received from one and only one of you, all 20 will equally split a large sum of money. If no letters are received, or more than one, no prize.
What would you to for a chance of winning the prize? What could you do in order to maximise the probability of winning?