Can you solve this math riddle?

The answer is.....(drumroll....)

42

Once again, you are right that we know no way of generating a truly random real number (what you name "an infinity of randomness"). On the other hand, refusing to work on real numbers because they cannot be written down in a finite time bears some similarity to refusing to solve (-3)*(-5)=? because one cannot buy a subzero number of eggs. We can simply imagine that it is possible and solve the riddle accordingly.

Suppose we have a group of N dice rollers, where N is some finite number. All of them take their first roll. If we eliminate everyone that did not roll the correct digit (3), then we expect to be left with N/10 dice rollers. Repeating for the second roll, we'll be left with N/100 rollers, then N/1000 after three rolls, N/10000 after four rolls, etc. In fact, after r rolls, the expected number of dice rollers left is N/(10^r). Since the target number (1/3) requires an infinite number of rolls, we can take the limit of N/(10^r) as r goes to infinity, resulting in zero. Therefore, for any finite number of dice rollers, we expect none of them to succeed in rolling the number 1/3.

So, N must be infinite.

More succinctly: because the target number requires an infinite number of success when the probability of each success is not 100%, the target is impossible to reach in a finite number of tries (each try being an infinite number of rolls).

Now, if you were to use 3-sided dice with the digits 0, 1, and 2, then only three people on average would be needed, since rolling a single 1 would succeed. The number 0.1 in base-3 is equal to the number 1/3 in base-10.

As soon as you introduce infinity into it,you place the math squarely in "imaginary"
As far as i can see,there has been no attempt to normalise the math by extracting the infinity.

Trust Einstein

The group would indeed have an infinite number of people, but can you figure out the size infinity the group would have? There are different sizes of infinity with the number of integers being the smallest size of infinity.

Infinite monkeys on infinite typewriters for infinity..yes..they may produce all of shakespear's works..but equally statistically valid they may come up with "a" to the power of infinity.All of them.

Come on now, the group must have at least 1 person to generate 1/3. It's easy: ONE PERSON WILL SUFFICE. What's the big deal about it?
Which do you think weighs the most 1 kg of cotton or 1 kg of iron?

Wrong analogy.

This is a statistics question,not a weight Vs mass question.

Statistically there is equal chance of infinite monkeys all typing consecutive "a" forever as them typing any other letter or combination of letters.

@lecctra

You are trapped in the "gambler's myth"