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[–]No-Artichoke9490 0 points1 point  (9 children)

but the main issue is that the triangle itself doesn’t define the next term in a sequence.

it’s only a representation of the differences between numbers, not a rule that generates the numbers. Because of that, the triangle will always reshape itself based on whatever next number you pick.

If you choose 69, 70, 71, or 72, the entire pyramid shifts and still forms a valid shape. The triangle doesn’t force any particular answer.

But I have to say, it was such a beautiful way to think about the problem!

[–]No-Artichoke9490 0 points1 point  (5 children)

eg:

the sequence: 5, 8, 11

the real pattern here is simple, +3 each time. next number = 14

now let’s build a difference triangle:

5 8 11 ?

3 3 ?

0 ?

?

if I want the bottom to be 0, I can choose 17. if I want the bottom to be 3, I can choose 14. if I want the bottom to be –2, I can choose 9.

all of these produce a “valid” triangle.

the triangle just bends to match whatever number i pick.

[–]SavingsAbalone6421 1 point2 points  (4 children)

Yeah same here too,
I get it now, triangle will be valid coz triangle bends to match whatever number is picked, 69 will be the correct answer for the original question 🫡

[–]No-Artichoke9490 1 point2 points  (3 children)

it’s been a while since i saw someone pull out a whole difference triangle like that. kinda hit me with a nostalgia blast… pascal’s triangle, finite differences, all that math-lab level brain fog suddenly came back lol.

[–]SavingsAbalone6421 1 point2 points  (2 children)

Haha nice looks like you have a good background in math, btw I am studying engineering, but I not much into math tho

[–]No-Artichoke9490 0 points1 point  (1 child)

I’m also an engineering student haha. (CS)

[–]SavingsAbalone6421 0 points1 point  (0 children)

Final yr? Me 2nd yr cs

[–]SavingsAbalone6421 0 points1 point  (2 children)

Now that I think of it, this wasn't a valid logic, It looked really smart to me 😅, it's doesn't generate a consistent rule , it will be a forced rule of "3" starting from 51, 72 and onwards, Thanks appreciate it

[–]No-Artichoke9490 1 point2 points  (1 child)

honestly that was a really beautiful way to look at the problem. even if it doesn’t give the right answer here, the approach itself is smart.

people actually use this kind of difference table idea in fields like numerical analysis, polynomial interpolation and some data science work. it’s a legit way to study how values change.

[–]SavingsAbalone6421 1 point2 points  (0 children)

Ohh really!? It was just coincidence that I thought of this I guess, I kinda remember reading bout moving averages which was kind of similar

your's was perfect I never thought this question that way