Yeah, I try to be as clear as possible in explaining the issue with Jamup and then make a sentence like that...
It'd make a great album title.
Just another update. Quote: "The cable adapter I bought didn't help." Actually it DID solve the problem. I first tried it by putting the stereo to mono adapter plug into the speaker but a few days later I thought I'd put the mono adapter into the iPad instead and, bingo!, it worked. So there's that fixed. (or at least it's a workaround)
Just a thought. Were you and your friend using stereo cables that were supplied with your speakers? And is the speaker a single one, ie. mono?
I have a possible scenario that might explain all your symptoms.
The iPad socket takes a 4 pole plug with the following assignments:-
Pole 1 (tip) left audio, Pole 2 right audio, Pole 3 ground, Pole 4 audio in.
Poles 3 & 4 short together when a 3 pole (stereo) plug is inserted so that stereo output still works.
I suspect your cable is a mono cable (2 wires) with a stereo plug on one, or both ends. Inside the plugs, I think that only poles 2 & 3 are connected to those wires, ie. only the right channel is active. I also suspect that Jamup is only putting out audio on the left channel (pole 1). This would mean no audio from Jamup, EXCEPT when you push the plug in further, at which point pole 2 on the plug touches pole 1 in the socket and lets left channel audio cross onto the right channel.
When you added your stereo to mono adapter at the speaker end of the cable, it connects poles 1 & 2 of the stereo plug, but there is no signal arriving at pole 1 (it's disconnected at one, or both ends), so it doesn't fix the problem. However, when you use the adapter at the other end, it connects poles 1 & 2 of the iPad socket, letting left channel audio onto the right channel, which IS connected in your speaker cable and BINGO, you have audio.
Obviously, I have made assumptions, any or all of which may be wrong.
That sounds reasonable. I'm surprised the option in Jamup to switch which left/right channel to send the signal had no effect to this strange problem. And yes, we both were using a mono speaker that came with a cable with stereo ends.