The above circuit was obtained from Alan Yate's page:

Alan Yates Ring Counter

$ 1 0.000005 14.235633750745258 44 5 50 5e-11
r 64 368 112 368 0 10000
R 64 368 32 368 1 2 200 3 3 0 0.5
t 112 368 144 368 0 1 -5.135592176334875 5.235592178845508e-8 100 default
g 144 384 144 432 0 0
t 320 432 288 432 0 -1 5.3615350109423945 1.093569627078561 100 default
t 288 496 320 496 0 1 -5.3615350109423945 1.5191081027469378e-7 100 default
w 320 432 320 480 0
w 288 448 288 496 0
r 288 496 288 544 0 10000
w 320 512 320 544 0
w 320 544 288 544 0
g 288 672 288 688 0 0
w 288 416 288 384 0
w 288 384 320 384 0
162 320 352 320 384 2 default-led 1 0 0 0.01
r 320 352 320 304 0 100
c 320 352 496 352 0 1e-8 0.7562632690591222 0
c 528 352 704 352 0 1e-8 4.41732030103937 0
r 528 352 528 304 0 100
162 528 352 528 384 2 default-led 1 0 0 0.01
w 496 384 528 384 0
w 496 416 496 384 0
w 528 544 496 544 0
w 528 512 528 544 0
r 496 496 496 544 0 10000
w 496 448 496 496 0
w 528 432 528 480 0
t 496 496 528 496 0 1 -5.361535009840701 1.5302363112593457e-7 100 default
t 528 432 496 432 0 -1 5.361535009840701 0.9822575137210956 100 default
c 736 352 848 352 0 8e-9 -1.674671540687966 0
r 736 352 736 304 0 100
162 736 352 736 384 2 default-led 1 0 0 0.01
w 704 384 736 384 0
w 704 416 704 384 0
w 736 544 704 544 0
w 736 512 736 544 0
r 704 496 704 544 0 10000
w 704 448 704 496 0
w 736 432 736 480 0
t 704 496 736 496 0 1 0.6604777284509364 0.6895211691227966 100 default
t 736 432 704 432 0 -1 -0.6604777284509364 -0.6892047834861982 100 default
w 320 304 528 304 0
w 528 304 736 304 0
w 144 352 144 304 0
w 848 352 848 256 0
w 848 256 288 256 0
w 288 256 288 384 0
w 736 304 864 304 0
r 864 304 912 304 0 270
w 912 304 944 304 0
w 944 304 944 416 0
t 1008 448 944 448 0 1 -6.0453982550762255 0.5930664181052041 100 default
w 944 416 944 432 0
c 944 464 944 560 0 0.000009999999999999999 5.36153532681857 0.001
r 320 432 384 432 0 10000
r 528 432 592 432 0 10000
r 736 432 800 432 0 10000
w 384 432 384 576 0
w 592 432 592 576 0
w 800 432 800 576 0
w 384 576 592 576 0
w 592 576 800 576 0
w 800 432 848 432 0
r 848 432 848 512 0 10000
r 1008 448 1008 304 0 10000
r 1008 448 1008 544 0 10000
v 1056 432 1056 304 0 0 40 12 0 0 0.5
w 496 352 496 384 0
w 704 352 704 384 0
w 944 464 912 464 0
w 912 464 912 432 0
w 912 432 848 432 0
w 320 304 160 304 0
w 160 304 144 304 0
w 288 640 288 672 0
w 496 544 496 640 0
w 496 640 288 640 0
w 704 544 704 640 0
w 704 640 496 640 0
w 848 512 848 640 0
w 848 640 704 640 0
w 944 560 944 640 0
w 944 640 848 640 0
w 1008 544 1008 640 0
w 976 640 944 640 0
w 1056 432 1056 640 0
w 288 544 288 640 0
w 1056 640 1008 640 0
w 1008 640 976 640 0
w 1056 304 1008 304 0
w 1008 304 944 304 0
d 352 384 368 384 2 default

Notice the NPN transistor that is driving the transistor bases, it is configured as an emitter follower with voltage divider input.  If I remove the transistor keeping the voltage divider, the counter still works.  So maybe the transistor isn't strictly necessary.  I am not sure.

And here is the falstad code:

$ 1 0.000005 14.235633750745258 44 5 50 5e-11
r 64 368 112 368 0 10000
R 64 368 32 368 1 2 200 3 3 0 0.5
t 112 368 144 368 0 1 -5.131476983752162 5.23147699261485e-8 100 default
g 144 384 144 432 0 0
t 320 432 288 432 0 -1 2.809708337000875 -0.5192943894697342 100 default
t 288 496 320 496 0 1 -2.809708337000875 0.5188950643520817 100 default
w 320 432 320 480 0
w 288 448 288 496 0
r 288 496 288 544 0 10000
w 320 512 320 544 0
w 320 544 288 544 0
g 288 544 288 560 0 0
w 288 416 288 384 0
w 288 384 320 384 0
162 320 352 320 384 2 default-led 1 0 0 0.01
r 320 352 320 304 0 100
c 320 352 496 352 0 1e-8 4.4080778843656825 0
c 528 352 704 352 0 1e-8 -1.6147684484980505 0
r 528 352 528 304 0 100
162 528 352 528 384 2 default-led 1 0 0 0.01
w 496 384 528 384 0
w 496 416 496 384 0
g 496 544 496 560 0 0
w 528 544 496 544 0
w 528 512 528 544 0
r 496 496 496 544 0 10000
w 496 448 496 496 0
w 528 432 528 480 0
t 496 496 528 496 0 1 0.6604406715906297 0.6893801520496559 100 default
t 528 432 496 432 0 -1 -0.6604406715906297 -0.6891667349998778 100 default
c 736 352 848 352 0 1e-8 1.2834719613713101 0
r 736 352 736 304 0 80
162 736 352 736 384 2 default-led 1 0 0 0.01
w 704 384 736 384 0
w 704 416 704 384 0
g 704 544 704 560 0 0
w 736 544 704 544 0
w 736 512 736 544 0
r 704 496 704 544 0 10000
w 704 448 704 496 0
w 736 432 736 480 0
t 704 496 736 496 0 1 -3.837873060390304 0.0015316565241440445 100 default
t 736 432 704 432 0 -1 3.837873060390304 -0.3683704157310528 100 default
w 320 304 528 304 0
w 528 304 736 304 0
w 320 304 144 304 0
w 144 352 144 304 0
w 848 352 848 256 0
w 848 256 288 256 0
w 288 256 288 384 0
w 736 304 864 304 0
r 864 304 912 304 0 270
w 912 304 944 304 0
r 320 432 384 432 0 10000
r 528 432 592 432 0 10000
r 736 432 800 432 0 10000
w 384 432 384 624 0
w 592 432 592 624 0
w 800 432 800 624 0
w 384 624 592 624 0
w 592 624 800 624 0
w 800 432 848 432 0
r 976 432 976 304 0 10000
r 976 432 976 544 0 10000
g 976 544 976 560 0 0
w 944 304 976 304 0
w 976 304 1056 304 0
v 1056 368 1056 304 0 0 40 12 0 0 0.5
g 1056 368 1056 416 0 0
w 496 352 496 384 0
w 704 352 704 384 0
w 976 432 848 432 0

 Maybe it's not that big of a deal to simplify the circuit by removing a single transistor, but I thought it was worth trying.  After all, ideally we can use minimal components.

The above circuits appear to work.  However, I have not (yet) physically constructed any of them.  My thought is that if it works in falstad, there is a good chance it will work in hardware.  OTOH, if it doesn't work in falstad, then I doubt it will work in hardware.

In addition, sometimes I will see momentary glitches such as two LEDs momentarily lit at the same time.  It's hard to know if this is coming from falstad or is authentic behavior.

CHAINING

It's one thing to make a ring counter work, and another thing to successfully chain them together such that the nth stage of oscillator 1 serves as the clock input pulse to stage 2.  I have not (yet) figured out how to accomplish that, but below is my best attempt.  The problem is that the clock pulse does not have the correct duty cycle.  Stage 2 advances, but in between no LEDs are lit:

falstad code:

$ 1 0.000005 10.20027730826997 50 5 50 5e-11
t 336 192 352 192 0 -1 0 0 100 default
t 320 208 304 208 0 1 0 0 100 default
w 304 192 336 192 0
w 320 208 352 208 0
r 352 208 352 240 0 10000
w 304 224 304 240 0
w 304 240 352 240 0
g 304 240 304 256 0 0
162 352 144 352 176 2 default-led 1 0 0 0.01
r 352 144 352 112 0 100
r 304 192 272 192 0 10000
w 272 192 272 288 0
w 272 288 416 288 0
w 416 288 560 288 0
w 416 192 416 288 0
r 496 144 496 112 0 100
162 496 144 496 176 2 default-led 1 0 0 0.01
g 448 240 448 256 0 0
w 448 240 496 240 0
w 448 224 448 240 0
r 496 208 496 240 0 10000
w 464 208 496 208 0
w 448 192 480 192 0
t 464 208 448 208 0 1 0 0 100 default
t 480 192 496 192 0 -1 0 0 100 default
t 624 192 640 192 0 -1 0 0 100 default
t 608 208 592 208 0 1 0 0 100 default
w 592 192 624 192 0
w 608 208 640 208 0
r 640 208 640 240 0 10000
w 592 224 592 240 0
w 592 240 640 240 0
g 592 240 592 256 0 0
162 640 144 640 176 2 default-led 1 0 0 0.01
r 640 144 640 112 0 80
r 592 192 560 192 0 10000
w 560 192 560 288 0
w 560 288 704 288 0
w 560 544 704 544 0
w 560 448 560 544 0
r 592 448 560 448 0 10000
r 640 400 640 368 0 80
162 640 400 640 432 2 default-led 1 0 0 0.01
g 592 496 592 512 0 0
w 592 496 640 496 0
w 592 480 592 496 0
r 640 464 640 496 0 10000
w 608 464 640 464 0
w 592 448 624 448 0
t 608 464 592 464 0 1 0 0 100 default
t 624 448 640 448 0 -1 0 0 100 default
t 480 448 496 448 0 -1 0 0 100 default
t 464 464 448 464 0 1 0 0 100 default
w 448 448 480 448 0
w 464 464 496 464 0
r 496 464 496 496 0 10000
w 448 480 448 496 0
w 448 496 496 496 0
g 448 496 448 512 0 0
162 496 400 496 432 2 default-led 1 0 0 0.01
r 496 400 496 368 0 100
r 448 448 416 448 0 10000
w 416 448 416 544 0
w 416 544 560 544 0
w 272 544 416 544 0
w 272 448 272 544 0
r 304 448 272 448 0 10000
r 352 400 352 368 0 100
162 352 400 352 432 2 default-led 1 0 0 0.01
g 304 496 304 512 0 0
w 304 496 352 496 0
w 304 480 304 496 0
r 352 464 352 496 0 10000
w 320 464 352 464 0
w 304 448 336 448 0
t 320 464 304 464 0 1 0 0 100 default
t 336 448 352 448 0 -1 0 0 100 default
v 912 352 912 304 0 0 40 12 0 0 0.5
g 912 352 912 368 0 0
r 912 304 912 272 0 270
w 912 304 864 304 0
w 352 112 496 112 0
w 496 112 640 112 0
w 352 368 496 368 0
w 496 368 640 368 0
w 640 112 800 112 0
w 912 240 912 272 0
r 864 304 864 416 0 10000
t 864 416 832 416 0 1 0 0 100 default
r 864 416 864 464 0 10000
c 832 432 832 464 0 0.000009999999999999999 0.001 0.001
r 784 432 784 464 0 10000
w 784 464 832 464 0
w 832 464 864 464 0
g 784 464 784 496 0 0
w 784 432 704 432 0
w 704 432 704 288 0
w 352 112 208 112 0
w 208 112 208 368 0
w 832 400 832 304 0
w 832 304 864 304 0
w 912 112 800 112 0
t 192 416 208 416 0 
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