5 ms·
5) sum of the single digits squared: (1+2+3+4+5+6+7+8+9)²
by _kb 2y ago
5) sum of the single digits squared:
(1+2+3+4+5+6+7+8+9)²
- umeshunni 2y agoSome more (thanks to chatgpt-o1) 6) sum of the first 45 odd numbers: 1+3+5+...+89 7) is a Harshad number: https://en.m.wikipedia.org/wiki/Harshad_number https://en.m.wikipedia.org/wiki/Harshad_number
- globnomulous 2y ago6 is kind of cheating. It's a restatement of 45^2. 3^2 is the sum of the first three odd numbers. 4^2 is the sum of the first four odd numbers. 5^2 is the sum of the first five odd numbers. Edit: sorry, don't mean to be a pill.
- xerox13ster 2y ago89 isn't 9^2, 81 is.
- mkl 2y agoHuh? 89 is the 45th odd number.
- bonzini 2y ago4 and 5 too
- globnomulous 2y agoHow so? I'm too dumb to see it.
- bonzini 2y agoThe sum of the first n cubes is always the square of the sum of numbers from 1 to n. For example 1³+2³+3³+4³=(1+2+3+4)². You can prove it by induction; just expand (n(n+1)/2)² – (n(n-1)/2)², the result is n³.
- fifilura 2y agoI don't consider it cheating, I bet most of these rules have an internal relation.
- roenxi 2y agoThey do indeed have an internal relation - they all add up to 2025. Obviously all the formula will be equivalent to each other. They are, by construction, all restatements of each other.
- mr_toad 2y agoI guess that means that every number is equivalent to a formula? Is there some sort of metric of how many formula produce the same number?
- layer8 2y agoYou’d have to at least exclude subtraction and division (and zero) to not have infinitely many formulas for every number.
- kdmccormick 2y agoI would say that a rule is "cheating" iff it is implied by another rule for any arbitrary N.
- freehorse 2y agoI think that it is a nice observation. Some people complain that explaining the formation of a rainbow scientifically makes it lose its "aweness" but I think it even deepens it. Actually, property 5) trivially implies 1) but also 2), as `(1+2+...+n)² = n²(n+1)²/4` and either n or n+1 must be divisible by 2 hence one of the squares divisible by 4 hence it is a product of squares. But also property 4) as `(1+2+...+n)² = 1³+2³+...+n³` (easy to show by induction).
- bratwurst3000 2y ago8) the sum of 2024 + 1 also
- nhatcher 2y ago(just reading wikipedia here, I didn't know about Harshad numbers) There is no such thing as a Harshad number, there is a _Harshad number in a given base_. All integers between zero and n are n-harshad numbers. Which is a pity, because apparenty it means the `joy-giver`. I think human kind could use a joy giver year
- keepamovin 2y agoOh I like these two.