SMBC Comics Forum

http://www.smbc-comics.com/comic/puzzle-time

I dunno, something's wrong with the artwork. I can't read any of them.

y = 0.9303569123 x^7 - 22.23193879 x^6 + 207.829112 x^5 - 961.3816793 x^4 + 2289.732664 x^3 - 2625.385296 x^2 + 1111.506783 x + 0.00001611345942

Graph on Wolfram Alpha

i got it as (521/560)x^7 - (2587/90)x^6 + (43291/120)x^5 - (170393/72)x^4 + (2085781/240)x^3 - (6369907/360)x^2 + (638962/35)x - 7219, but to each their own, i guess~

My version is essentially the same, but rendered as:
( 4689 * n^6 - 112049 * n^5 + 1047459 * n^4 - 4845365 * n^3 + 11540256 * n^2 - 13231946 * n + 5601996 ) * n / 5040

(The next term is 8666.)

https://oeis.org/search?q=0%2C1%2C4%2C- ... &go=Search

If he was just randomly thinking "I wonder what sequence hasn't been used before..." then he really nailed it.

Psssh, that's easy.

f(0) = 1
f(x) = 0 when x != 0

f(x-1)*1+f(x-2)*4+f(x-3)*-13+f(x-4)*-133+f(x-5)*52+f(x-6)*53+f(x-7)*-155

See? Simple! <.< >.>

I'm personally fond of the form
f(n) = ₙC₁ + 2 ₙC₂ − 22 ₙC₃ − 61 ₙC₄ + 552 ₙC₅ − 1940 ₙC₆ + 4689 ₙC₇.

Woom wrote:My version is essentially the same, but rendered as:
( 4689 * n^6 - 112049 * n^5 + 1047459 * n^4 - 4845365 * n^3 + 11540256 * n^2 - 13231946 * n + 5601996 ) * n / 5040

(The next term is 8666.)

I just used matlab to get an estimate of the coefficients via polyfit (obviously I had to specify degree 7 since that's the "simplest" polynomial that fits these parameters, though there are infinitely many polynomials of greater degree that also fit this sequence).

Anyway, I concur that the next term is 8666 in the case that we assume the simplest possible pattern fit to the sequence. But let's be honest, there's no author intention because I doubt zach knows how to fit a polynomial to a set of points

Someone should definitely submit it on oeis as the weinersmith numbers.

The obvious solution is the sequence defined as follows:

The sequence an is defined by:
{a1 = 0
a2 = 1
a3 = 4
a4 = -13
a5 = -133
a6 = 52
a7 = 53
a8 = -155} for an from N.

Yes, I am a dickhead. My area is pure mathematics; answers that are technically true but completely meaningless are what I do best.

cmena2702 wrote:The obvious solution is the sequence defined as follows:

The sequence an is defined by:
{a1 = 0
a2 = 1
a3 = 4
a4 = -13
a5 = -133
a6 = 52
a7 = 53
a8 = -155} for an from N.

Yes, I am a dickhead. My area is pure mathematics; answers that are technically true but completely meaningless are what I do best.

I am willing to believe that your area is pure mathematics because anyone *sane* would be 0-indexing this sequence ;P but regardless, you seem to have missed the comma+ellipsis in the original sequence. This directly implies that the sequence has length greater than 8. Many even use it to imply that the sequence is infinite (perhaps repeating, but still infinite), but at the very least, not even a theoretical mathematician would put an ellipsis after the end of a finite sequence.

I'll take my 14 points please.

{n∈Z|(∃x∈N)[n=H(x-1)+3H(x-2)-17H(x-3)-120H(x-4)+185H(x-5)+H(x-6)-208H(x-7)]}
Where Z are the integers, N is the set of natural numbers, and H is the Heaviside function.

DrHammer wrote:I'll take my 14 points please.

{n∈Z|(∃x∈N)[n=H(x-1)+3H(x-2)-17H(x-3)-120H(x-4)+185H(x-5)+H(x-6)-208H(x-7)]}
Where Z are the integers, N is the set of natural numbers, and H is the Heaviside function.

Hahah, okay, I bow to you, that was a perfect answer.

And all future elements are -155. So elegant! You won't even introduce nonintegers!

Hi. There's another kind of puzzle, such as wooden puzzle models, a great way to show your creative side as well as having a beautiful object to display at home or in the office. Not only are they fun and challenging to build, they are also designed with all the mechanics needed to make them move like the real objects they represent.

Wooden model kits make a great gift for friends and family who appreciate creating functional works of art.

When you assemble wooden models the creative side of your brain gets the exercise it needs. Creating a scale model is a whole art, and while you can follow the instructions exactly or paint the model in a historically accurate style, you can also go beyond and bring your own style. There is no right or wrong way to create a model - it all depends on your personal preferences and what you hope to get out of it.