Crazy Hard Math Problem #1

ev3coolexit987654

t = 0.5(x^2 + x)

gtoal

bobbybee wrote:
Didn't Gauss solve this, what is it, hundreds of years ago? When he was, like, 9?

n(n+1)/2

No, that's the formula for the sum of the numbers 1..n. The problem here was Pascal's Triangle.

Superdoggy

gtoal wrote:
bobbybee wrote:
Didn't Gauss solve this, what is it, hundreds of years ago? When he was, like, 9?

n(n+1)/2

No, that's the formula for the sum of the numbers 1..n. The problem here was Pascal's Triangle.

Actually, no, sorry, it wasn't.

The question asks for N cans in the bottom row, how many cans total are there assuming the cans are stacked in a triangle. So the question pretty much is asking for the formula for the sum of numbers 1…n.

Hardmath123

Can't use ellipses, huh? Here's a related problem: you're now stacking them like this

  .  
 ... 
.....

For any prime number p, can you make two towers like this—not necessarily the same height—so that the total number of “cans” is p? If not, for which primes does this work? Use ellipses to solve. Leave me a comment.

iamunknown2

Hardmath123 wrote:
Can't use ellipses, huh? Here's a related problem: you're now stacking them like this
  .  
 ... 
.....
For any prime number p, can you make two towers like this—not necessarily the same height—so that the total number of “cans” is p? If not, for which primes does this work? Use ellipses to solve. Leave me a comment.

?
All I know is that you're adding up 2 square numbers in this case.

Econinja

Super Easy: 1+2+3+4+5 obviously

= 15
Not So Easy: Used a script in a project

which would equal 1+2+3+4+5… to 457 = 104653
Insane: I'm not good at that!

__init__

Hardmath123 wrote:
Can't use ellipses, huh? Here's a related problem: you're now stacking them like this
  .  
 ... 
.....
For any prime number p, can you make two towers like this—not necessarily the same height—so that the total number of “cans” is p? If not, for which primes does this work? Use ellipses to solve. Leave me a comment.

I can tell already that the answer is no:

lowest      =  .    .  (2 stacks with only one can) = 2 (prime)


next lowest =  .    .   (1 stack with 1 can, 1 stack with 4) = 5 (prime)
                   ...

we just skipped 3 there.

Hardmath123

Sure, but can you characterize primes that *do* work? Is there only a finite number of such primes? Or maybe everything except 3 works?

bobbybee

Hardmath123 wrote:
Sure, but can you characterize primes that *do* work? Is there only a finite number of such primes? Or maybe everything except 3 works?

The set intersection of 2x(x-1) + 1 and the primes, where x is a positive integer.

I think

Last edited by bobbybee (Aug. 12, 2015 20:55:54)

Hardmath123

Can you name an element of that set?

bobbybee

Hardmath123 wrote:
Can you name an element of that set?

5, 13, 41…

Hardmath123

What's true about all those numbers?

Can you name some elements outside that set that work?

(It's hard to do the whole socratic thing over fora…)

ev3coolexit987654

Hardmath123 wrote:
Sure, but can you characterize primes that *do* work? Is there only a finite number of such primes? Or maybe everything except 3 works?

The intersection of x^2+y^2 and the primes where x and y are positive integers
5, 13, 41, 61, etc

lucyk2354

I know, gauss did solve it! You just do it like this:
biggest + smallest * biggest/2 and figure out if you need to add the middle number.
Most people won't get this

DadOfMrLog

bobbybee wrote:
Didn't Gauss solve this, what is it, hundreds of years ago? When he was, like, 9?
n(n+1)/2

Yes, he did.

The story goes that a teacher set the class the task of finding the sum of integers from 1 to 100 - to keep them quiet for a while.

Gauss came back with the answer a minute or two later…

A CHALLENGE
============

Above is an easy and well-known one these days, but here's something that you might find a bit more of a challenge (I had fun solving this when I was at school):

Given any number that's a positive integer, find the list of all the ways you can get that number by summing consecutive positive integers (where each sum must have more than one integer, so the list doesn't include just the number itself).

For example, the number 20 can only be summed as 2+3+4+5+6 - no other sum of consecutive positive integers will make 20.

However, 25 can be summed as both 12+13 and as 3+4+5+6+7 (but those are the only two ways to do it).

Even better, write a Scratch project that does it - i.e. ask the user for an integer, give back all sums of consecutive integers that give that integer.
(Note that I'm expecting this to work for any size integer that Scratch can handle [let's say up to 14 digits], so you'll have to do better than just searching through all possibilities… ;D )

Have fun! xD

Last edited by DadOfMrLog (Oct. 17, 2015 10:03:42)

WooHooBoy

DadOfMrLog wrote:
bobbybee wrote:
Didn't Gauss solve this, what is it, hundreds of years ago? When he was, like, 9?
n(n+1)/2
Yes, he did.

The story goes that a teacher set the class the task of finding the sum of integers from 1 to 100 - to keep them quiet for a while.

Gauss came back with the answer a minute or two later…

A CHALLENGE
============

Above is an easy and well-known one these days, but here's something that you might find a bit more of a challenge (I had fun solving this when I was at school):

Given any number that's a positive integer, find the list of all the ways you can get that number by summing consecutive positive integers (where each sum must have more than one integer, so the list doesn't include just the number itself).

For example, the number 20 can only be summed as 2+3+4+5+6 - no other sum of consecutive positive integers will make 20.

However, 25 can be summed as both 12+13 and as 3+4+5+6+7 (but those are the only two ways to do it).

Even better, write a Scratch project that does it - i.e. ask the user for an integer, give back all sums of consecutive integers that give that integer.
(Note that I'm expecting this to work for any size integer that Scratch can handle [let's say up to 14 digits], so you'll have to do better than just searching through all possibilities… ;D )

Have fun! xD

note that 2^n for each solution has no solution.

Last edited by WooHooBoy (Oct. 17, 2015 11:12:59)

DadOfMrLog

WooHooBoy wrote:
DadOfMrLog wrote:
A CHALLENGE
…
note that 2^ns don't work….

Well spotted! -did you find that by trying out with various numbers, or did you work out a way to find the list?

But are powers of 2 the only numbers with zero length list of sums?

Can you find any other numbers like that? Or can you prove that powers of 2 are the only numbers with that property?

Last edited by DadOfMrLog (Oct. 17, 2015 11:23:25)

Zro716

DadOfMrLog wrote:
Or can you prove that powers of 2 are the only numbers with that property?

you can't factorize powers of two with any other number than other powers of two, and because consecutive sums must have at least 1 odd operand, this presents an impossibility.

MegaApuTurkUltra

-Incognito- wrote:
________________________________________________________________________________________________________________________
Hey Scratchers,
crazy idea popped in my head while I was watching Numbers (best show of all times, I suggest that everyone here start watching the series on Netflix.)
I wanna know how many people out there have iq's higher than a cardboard box, like math as much as I do, and know their stuff.
Every week, I'm gonna post some ridiculously insane math problems… so hard that they just might keep you up at night.
Feel free to rage quit

And remember… Never underestimate what the brain can do
If you Have the answers to some of the questions Post BELOW

Mathematically yours,
-Incognito-
________________________________________________________________________________________________________________________

#1 THE PYRAMID PROBLEM

Mary stacks cans of tomatoes in a triangular pyramid like so: __
| |
|__|
__ __
| | | |
|__| |__|
__ __ __
Bottom Row ——–> | | | | | |
|__| |__| |__|

Super Easy Question:
If there are 5 cans in the bottom row, how many cans are there in total?

Not-So-Easy-Question :
If there are 457 cans in the bottom row, how many cans are there in total?

INSANE QUESTION:
Make a formula for total t cans given x amount of cans in the bottom row
Note: (You CANT use ellipses)

1. 15
2. 104653
3. (x+1)*x/2

Am I missing something? This is easy…

NoMod-Programming

Edit: wrong topic…

Last edited by NoMod-Programming (Oct. 24, 2015 01:41:22)

Discuss Scratch