That seems complicated.
Average is (100+1)÷2= 50.5
50.5 average x 100 numbers = 5050.
You did essentially the exact same thing in a different order.
(100+1)÷2 × 100
(100+1)x100 ÷ 2
Clever though
The neat thing about math is that you can generally find several different paths to the same solution, and go with whichever is most intuitive to you.
Though sadly ime that is what teachers usually completely fail to convey. And then we wonder why so many people hate math.
I think you’d need to prove that the average is (100+1)/2 because that’s not an axiom.
… am I the only one who learned 1+100, 2+99… to make 101 times 50 pairs? Lmao feels like it’s much easier. 101 × 50 = 5050
I’d say it’s fifty-fifty.
The math is the same, you just wrote it more “casually”. For me it was 0+100, 1+99, 2+98 … 49+51 -> 100 x 50 = 5000, then add the 50 that was missed from the middle for 5050. But yeah I remember coming up with that when I was really young.
This is my first time seeing this problem. Interesting that they taught it in school.
Had a statistics and probability class in hs instead of the standard precalc. I feel it’s more applicable for students now than precalc anyways. It felt pretty cool to sit down in class and figure out the odds of winning on a lotto ticket and when the odds indicate you should buy a ticket.
Yeah pre-calc is pretty much remedial math nowadays. You don’t even get 100 level math until you’re at intermediate algebra!
Thinking of it in terms of statistics makes a lot of sense, I can see how this problem would help develop intuitions.
I always thought like that:
Hmmm: 1 + 2 + 3 + … + 99 + 100
Kommutativgesetz be like: This equals:
100 +1 + 99 + 2 +98 + 3 . . . And this equals: 101+ 101+ 101+ . . .How often do I need to do this? I use up 2 numbers for each 101. I have 100 numbers total. So that’s 50x101.
Now you can think about: What if it’s 1000 instead of 100? But it#s easy from here…
Ohhhhh
Ah yes, because the goal of teachers is to make their students waste a lot of time.
Well, it does happen
IIRC, In this case the teacher tried to get smart ass Gauss shut up for a bit so he could teach the other students. It was only Gauss that had to solve the problem.
Is it required to wear a silly hat to be a genius mathematician? I’ve seen Euler and his hat. But I didn’t realize Gauss was in on it too.
Seeing this meme gives me flashbacks to the 10 Deutschmark bill (I think that was the one)
Just put it in the calculator.
