Yep

Looking at a site and it has 2 3 5 12 as the hardest one by their methodology.

Funny. I got that one right away, but was stumped as **** on the 4/9/10/16 and 4/4/7/7.

So one site I was looking up threw in 3 4 9 10. But with the caveat that 3 4 9 10 needs to include exponential. I've been thinking about this but don't have an answer.

With several math gurus in this thread I am a bit surprised that many of you folks have not gotten hooked on Triplechain. I think I am one of the few TripleChain players without a strong background in math.

Ibavly used to play, and Xander has dabbled a bit, but I am not sure if housenuts, chuckles, lattimer, eyebooger, e_holle, iraisetoomuch et al have ever give TripleChain a try..??

I think I looked at it a while back and wasn't that interested.

I played for a solid 4 or 5 months.

For the most part the strat in the triplechain thread is over my head

I am not improving and my personal best/daily challenge ranking will only improve as a result of luck

I would likely revisit it if more basic strat was put in the thread

See post 5846 and then 5844 and 5845. I have received feedback from newbs via PM that these posts have been helpful in starting a plan to get up to speed on the basics of TripleChain more quickly.

My whole goal was to make something introductory that would give enough info to get people going on the right track sooner, but not so much info as to reveal some tactical things it took people a while to figure out....

Thus the focus on opening strategy and the main opening lines...

Zac (the site owner) supported this and has made a link to post 5846 in the Help (Getting Better) section on the Triplechain site.

cool... under what handle?

You folks can see I am on a mission to recruit new blood. lol
It is nice to have 30 to 35 regs

So I'm doing simultaneous equations with a class in school and we get talking about the sorts of equations that will give 3 sets of solutions. More specifically Equation 1 is a circle and what can equation 2 be so that there are 3 sets of solutions.

We've come up with type 1 where there is a turning point as equation 2 meets to circle



and we've come up with type 2 where you have a graph that double back over itself so that there are only 3 solutions



And I'm sure there's at least a type 3, "where there is a discontinuity in the graph" but I can't come up with an example that works. I know I could manually restrict the domain, but I'm not looking to do that.

Anyone got any ideas?

Here's a great online graphing tool that you could play around with: https://www.desmos.com/calculator

I'd also be very interested to hear about different types of graphs that give an odd number of intersections

Something like

1/x

and

(x-1)^2+(y-1)^2=8

?

that's the same as type 1 to me

I'm looking for a graph that goes into the circle but doesn't come out

but I just played around with some implicit functions that involved roots, would still be interested if anyone has a simpler example

Found a curve such there a circle with k intersections for all integers (odd and even) k and has an easy equation.

Would you count touching the circle 3 times as a tangent as different from type 2?

I would count it as a different type and would be interested to see the example

I'm not the greatest mathematician, but I know enough to teach it to young students and I'm interested in a lot of it too

I think that must count for something

Just do a circle of radius 1 at (0,0)

Yeah, but it would be great to use a graph that is defined by a proper equation, not multiple, unrelated, restricted domain equations. Inscribe a triangle if you want to cheat. For xander's type 3 situations, most of the good stuff will be best represented in polar coördinates, like an Archemedian Spiral or a cardioid.

One man's cheat is another man's eureka moment

I like all the answers suggested

Fine,



Of course would be easier to just restrict the domain than doing tricky with absolute values

I'm sure there is a way to make like an 8th degree polynomial do something similar

For sure. Polynomials and conic sections and sinusoids are great examples to use for type 1. I'm trying for xander's other types, with three non-tangential intersections.

Less of a puzzle and more like a math problem, but have fun with this one:

Also while you're at it you can prove that an irrational number to the power of an irrational number can be rational