Why a 7→15 balancer is trivial to build

[golfmiketango]

For my soon-to-be published steel megasmelter design, I needed an absolutely count-perfect 7→15 balancer. Think that's hogwash? So did I, at first. But after many experiments with half-measures, and thinking over the numbers more carefully, I came to accept that, yes, without question, I absolutely required a count-perfect 7→15 balancer or my smelter design would simply never work properly.

My early attempts at 7->15 balancing were absolutely hilarious UPS-gobbling disasters. I believe my first "successful" implementation took a 7→8 balancer from the wiki, whacked each output into one full splitter of a standard 16→16 balancer, and then, from there, tacked on a custom-built 16→15 balancer.

Reading the numbers in the above paragraph, you may have already realized why any design like my prototype was so incredibly dumb. There is a far, far easier means to build this contraption. I'll put the solution in a spoiler in case you haven't thought of it, yet, but want to take a moment to try and puzzle it out on your own:

solution

Eventually, I realized this was an absolute head-slapper with a trivial solution. Plenty of designs for an 8→8 balancer exist. If I just tack a splitter onto each output belt, I now have a perfectly respectable 8→16 balancer and now I just loop an output into an input, and—voila!—a count-perfect 7→15 balancer has appeared.

Lesson learned: (2ⁱ-c)→(2ⁿ-c) balancers are basically all trivially stolen from other people's balancers for small c. By the same mechanism, any elegantly designed balancer is a damn good starting point for a balancer with one or two less inputs on each end. Everyone who's screwed around with balancers already kind-of knows this but—well, you actually have to think of using the technique, when you need it, to benefit from that knowledge. This insight is probably the most important bit of "secret sauce" (aside from experience with spaghetti hacks) required to construct those seemingly impossible balancer designs involving input/output counts with larger prime factors. The ability to instantly cook up wierd balancers this way will amaze your MP teammates....

So, without further ado, based on the above insight, here is a nice, compact, reasonably ups-efficient 7->15 balancer design that I was able to adapt (sort-of... a functional equivalent was used based on KillCreek2's compact 0.15+ 8→8) for my mega-smelter:

Easy game

7_15_balancer.png (1.02 MiB) Viewed 2828 times

Blueprint: (nb: "select all" may be broken in code blocks nested in spoilers, just do it manually!)

Code: Select all

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[BenSeidel]

Nice.