3 is the magic number

What percentage of numbers contain at least one digit that is a 3 ?

a. between 0 & 10
b. between 0 & 100
c. between 0 & 1,000
d. between 0 & N (as N >inf)

@Paul-Martin
You idiot - this is a chess site not a math site!

@Paul-Martin said
What percentage of numbers contain at least one digit that is a 3 ?

a. between 0 & 10
b. between 0 & 100
c. between 0 & 1,000
d. between 0 & N (as N >inf)

@Arkturos said
Hmm -- some life in this forum!

a. 10%
b. I nearly fooled myself, but 10%
c. By intuitive analogy, I'm thinking also 10% (please don't ask me to show my work)
d. Please see my answer to "c."

@Paul-Martin said
b. 19%
3, 13, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 43, 53, 63, 73, 83, 93

@Paul-Martin said
What percentage of numbers contain at least one digit that is a 3 ?

a. between 0 & 10
b. between 0 & 100
c. between 0 & 1,000
d. between 0 & N (as N >inf)

@Arkturos said
New approach: you didn't specify integers, so the answer for each range is 50%. 😉

@Paul-Martin said
OK
integers only

A month later, and nobody's answer has convincingly surpassed mine. 😉

@Arkturos said
A month later, and nobody's answer has convincingly surpassed mine. 😉

@Suzianne said
Are you @Metal-Brain?

@Arkturos said
Hmm -- some life in this forum!

a. 10%
b. I nearly fooled myself, but 10%
c. By intuitive analogy, I'm thinking also 10% (please don't ask me to show my work)
d. Please see my answer to "c."

@Paul-Martin said
What percentage of numbers contain at least one digit that is a 3 ?

a. between 0 & 10
b. between 0 & 100
c. between 0 & 1,000
d. between 0 & N (as N >inf)

@Paul-Martin said
The answer to 'd' is ... 100%

@moonbus said
By that logic, 100% is also the answer to the question "what percentage of numbers contain at least one digit wh/ is a 4, or a 5, or a 6...", too. And that cannot be right, not all simultaneously anyway. So the question arises, whether it makes any sense to talk about a percentage (any percentage) of infinity, as if infinity were itself a fixed quantity.