CD 4017 Reset Issue

Hi, I have built the attached circuit which works, except for one issue. If the outputs of each 4017 are connected to LED's they all light up, and that is fine.
The problem is that I have to connect outputs from each 4017 together, so that they light up in a predetermined sequence.
For example, the output from pin 3 on the first counter, must be connected to output 6 of the second counter. Other examples are pin 2 of the first counter must connect to pin 5 of the second, and pin 4 must combine with pin 1. This is shown on the schematic. (apologies it is drawn using Excel)
The connection of these pairs of wires all work, except for Pin 3 of the first 4017 with Pin 6 of the second.
What happens when I connect these outputs is that all the led's stop blinking, except for the output from 4017 (1) which stays on.
I can't help thinking that the output of pin 3 of 4017 (1) is being messed up by the reset signal of pin 15 on 4017 (2)
Any help on how to overcome this will be greatly appreciated

First, you need a resistor in series with each LED to limit the current in each output of the CD4017. This will save both the output circuitry on the cd4017 AND the LED itself.

Now for your question. Remember that an LED is a diode first and foremost. That means current only flows in one direction and, typically, no more than 5v should be applied in the reverse direction of these Light emitting DIODES. To overcome, you can put a small-signal diode like 1N4148, 1N914 or simple 1N4001 diode in "anti-parallel" with each LED in those three circuit paths where the output of CD4017 connects to another CD4017 output.

This antiparallel LED gives a path for the circuit to complete.

Your current reset issue may be because you are applying too much reverse current to the LED and attempting to draw too much current from a CD4017 and it is resetting. Or, you are essentially "shorting to ground through an LED" at one or more outputs because there is not a current limiting resistor as mentioned above.

Remember, the outputs of a CD4017 are never "off" or disconnected. They are "low" meaning they are essentially connected to ground.

Thank you gophert. I tried you diode suggestion, and it made no difference to my original problem. But nevertheless I thank you for taking the time to assist me