Apology and first puzzle
OK, that last entry will not be typical of my stuff. (It took me over an hour to write.) I was trying to get exposure from the "pop culture" crowd, but that's definitely not my final aim. So with that, I give you my first, math-related puzzle.
I have a six-sided die, with sides numbered from 1 to 6, perfectly normal except for being loaded. I roll the die, perhaps repeatedly, until it shows a number with a certain property. The way the die is loaded, the expected values of certain groups of numbers also have certain properties, as follows:
The expected value (EV) of a square number ("square" for short) is a triangular number.
The EV of a triangle is square.
The EV of a prime is composite.
The EV of a composite is prime.
For some a and b, the EV of a or b is exactly a/b.
What are the probabilities of each number?
I have a six-sided die, with sides numbered from 1 to 6, perfectly normal except for being loaded. I roll the die, perhaps repeatedly, until it shows a number with a certain property. The way the die is loaded, the expected values of certain groups of numbers also have certain properties, as follows:
The expected value (EV) of a square number ("square" for short) is a triangular number.
The EV of a triangle is square.
The EV of a prime is composite.
The EV of a composite is prime.
For some a and b, the EV of a or b is exactly a/b.
What are the probabilities of each number?