Here's something I've been thinking about recently.
{2,4,9} is an example of a set where:
>Each element is a digit 0-9
>the sum of any two or more digits modulo 10 is not in the set
What I'm wondering is, what is the maximum cardinality of such a set, and what are those sets with that cardinality? How can this be proven?
I got thinking about this after remembering a pic that some friends were sharing on Facebook when I was a teen.
It said something like "what's your fine?" and had a list of various naughty acts, each with a "fine" next to them.
It would be things like
>Kissed someone: $10
>Stolen something: $20
>Given a blowjob: $5
>Had sex: $12
Most of the fines would be a multiple of $10, with some exceptions. In the above scenario, if someone's answer ended in a 2, 5 or 7, I would know if they'd given a blowjob, had sex, or both, and 13-year-old me would get a kick out of it.
{2,4,9} is an example of a set where:
>Each element is a digit 0-9
>the sum of any two or more digits modulo 10 is not in the set
What I'm wondering is, what is the maximum cardinality of such a set, and what are those sets with that cardinality? How can this be proven?
I got thinking about this after remembering a pic that some friends were sharing on Facebook when I was a teen.
It said something like "what's your fine?" and had a list of various naughty acts, each with a "fine" next to them.
It would be things like
>Kissed someone: $10
>Stolen something: $20
>Given a blowjob: $5
>Had sex: $12
Most of the fines would be a multiple of $10, with some exceptions. In the above scenario, if someone's answer ended in a 2, 5 or 7, I would know if they'd given a blowjob, had sex, or both, and 13-year-old me would get a kick out of it.
