Connect multiple in/outputs in predefined order (beginner question)
Well, if you have that many pedals, you'll need a lot of switches, whatever type. I presume that both the pedal's input and output are low-power audio signals, correct me if I'm wrong.
What are your options?  


A lot of relays. Which you don't want, probably because they are bulky and expensive. But power relays are not made to switch signals in the first place.  
The reed relays I talked about in my answer to your previous question. These are cheaper, less bulky and fit for switching signals.  
Analog integrated switches. These were also mentioned in answers to this recent question. Solid-state.  
Analog multiplexers. Also mentioned in the answers to that question. This would considerably reduce the number of parts. (Olin rightly mentions 400 relays...)  
Crosspoint switches. Fair warning: these are expensive! But then you'll only need a few of them. They have a number of inputs (often 8 or 16), a number of outputs (also often 8 or 16) and a matrix which allows connections from one input to an output. They're expensive because most are spec'd for HF operation (video signals). I have yet to see one for audio. A solution with the analog multiplexers would come closest to that. (The most expensive part in this Analog Devices list is USD 300! A 16x16 switch is still more than USD 75. What I said: expensive)