Unutterably Silly Quiz

[poohbear_nc]

Originally Posted by Stitchawl

Plastic?????? I thought you were older than that!

"My" Lincoln Logs were made of wood stained brown. The flat roof boards were stained green! They even caused splinters sometimes!


Stitchawl

Indeed - mine were wood too! With splinters!

[I couldn't find a quick link to the original set - just the "new-fangled" plastic version! ]

Originally Posted by dreams

I remember a set at my grandmother's house and the "logs" were of wood. I think they were in a cylindrical can and my brothers and I had lots of hours of fun playing with them.

Originally Posted by Stitchawl

Plastic?????? I thought you were older than that!

"My" Lincoln Logs were made of wood stained brown. The flat roof boards were stained green! They even caused splinters sometimes!


Stitchawl

Oh my yes. Plastic Lincoln Logs? When was such a travesty allowed? How can one think of building Lincoln's log cabin with plastic? I wish I still had my set, complete with the cylindrical container with the metal screw top.

Speaking of toys from long ago did anyone else ever have a set of American Plastic Bricks™ by Elgo Plastics Company?



Even cooler that Lincoln Logs in the sorts of buildings one could construct.



So anyway I think it is time for one of the always popular math questions. Who out there is as smart as a 3rd Grader? The story supposedly is that when Carl Friedrich Gauss was in the 3rd grade his instructor, probably intending to keep the class busy doing sums for a while, assigned the problem of calculating the sum of all natural numbers 1 to 100. The instructor was stunned when Gauss a few moments later presented not only that sum, but a general formula for the sum of natural numbers from 1 to N for any number N. Gauss supposedly figuring out that formula in that short interval.

So that is the question. Provide a formula for the sum of natural numbers 1 to N, 1+2+3+ . . . +(N-1) +N, and prove that it holds for all numbers N.

[poohbear_nc]

{sigh - off to Google "natural numbers" - it's been a long time since the 3rd grade}

[Stitchawl]

Yeah man! I can do it!!!! 1+1 is 2... Yessssssssssssssss!
What's a '2?'


Stitchawl

Originally Posted by poohbear_nc

{sigh - off to Google "natural numbers" - it's been a long time since the 3rd grade}

Sorry I do not want terminology to be a barrier to all the clever people out there. The natural numbers are simply the counting numbers: 1,2,3,4, . . . ∞

[issybird]

N/2 X (1+N)

Can't prove it, though.

(I had my own Gaussian moment in school, but it was later than the third grade)

[pdurrant]

Write out all the numbers 1...N in order. Write them all out in reverse order. Ann the rows together. Obviously the total of each colum is (N+1) and the full total is Nx(N+1). But we want half that. N/2x(N+1). Issybird has the right answer.

  1     2     3   .... (N-2) (N-1)   N
  N   (N-1) (N-2) ....   3     2     1
========================================
(N+1) (N+1) (N+1) .... (N+1) (N+1) (N+1)

HTH

Originally Posted by issybird

N/2 X (1+N)

Can't prove it, though.

(I had my own Gaussian moment in school, but it was later than the third grade)

Yes!

Originally Posted by pdurrant

Write out all the numbers 1...N in order. Write them all out in reverse order. Ann the rows together. Obviously the total of each colum is (N+1) and the full total is Nx(N+1). But we want half that. N/2x(N+1). Issybird has the right answer.

  1     2     3   .... (N-2) (N-1)   N
  N   (N-1) (N-2) ....   3     2     1
========================================
(N+1) (N+1) (N+1) .... (N+1) (N+1) (N+1)

HTH

Well done. I would have also accepted a proof by Mathematical Induction. Your derivation and proof was supposedly the one offered by a very young Gauss. For that alone I guess it would rate as being more elegant.

So I would say either Issybird or Pdurrant should offer the next question, whoever does so first.

[SneakySnake]

[pdurrant]

Originally Posted by SneakySnake

OK, a numbers puzzle anyone should be able to answer. I suspect it'll be the quickest on the buzzer:

How many times can you subtract 5 from 25?

[poohbear_nc]

Originally Posted by pdurrant

OK, a numbers puzzle anyone should be able to answer. I suspect it'll be the quickest on the buzzer:

How many times can you subtract 5 from 25?

once ....

[poohbear_nc]

b/c then you would be subtracting 5 from 20, then from 15, etc. Hah! Saw right thru that one! [Errrr .... right?]

[Stitchawl]

Originally Posted by SneakySnake

You and me, babe... I got a big kick out of the "Obviously" in Paul's post!

... then comes a number question I can actually answer, and I'm too late! Pooh got it first.


Stitchawl

[poohbear_nc]

OK - a NON math question:

It is a substance whose structure is a polymer formed by cross linking of polyvinyl alcohol with a boron compound. It can be made at home from polyvinyl-alcohol-based glues, such as Elmer's Glue. It is a non-Newtonian fluid whose combination of fluid-like and solid-like properties makes it a Maxwell solid.
It is a toy.

What is it?

[SneakySnake]

slime?