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Start small with 2 or 3 and add later when needs and money dictate.
Farnell do volume discounts if you buy a few:
| Quantity | List Price |
|---|---|
| 1 - 2 | £33.96+VAT |
| 3 - 9 | £30.74+VAT |
| 10+ | £28.25+VAT |
So if you can afford 3-5 then you get a small discount, but you would need to buy a lot more to get a bigger discount.
It's unlikely you'll get a large enough discount to enable you to buy 15 if you can only afford a maximum of 5 at the moment as they are already very well priced for what you get.
As clem57 has already said, it might be best to start off with the 3-5 pi's you can afford to do, get the proof of concept working and then expand it to more when you can afford it.
Please blog about your progress on here though, it might help get you some good ideas and vital feedback on what you are doing 
Best Regards,
Rachael
Thank you very much. I knew that Newark did large quantity discounts on Pi's but I didn't know that Farnell had even better discounts. Thanks I will check it out. I also was going to test this on three raspberry pi's first before I did anything else. Thanks!!! That was very helpful.
Thanks I will do that first. Thanks!!!
Just an after thought, you may want to consider the Pi Zero. It only has one core, but they take less space. At $5 dollars apiece at Micro center, not a bad deal. Once catch, they only sell one at a time. You will also need to solve the lack of Ethernet and only micro USB connection. But that makes the project more fun solving the engineering problems.
You've got a funny idea there, clem! For "computing" there is not much "external" stuff you need except for a networking connection. So just plugging a cheap ethernet adapter into each pi zero should do the trick. Get yourself a TTL-serial adapter for configuration and debugging until the ethernet works....
To be honest I would rather use a RPi3 than a pi zero for the sheer power. I appreciate the idea but I think I am already on the right route. Thanks though!!!
Yes I agree. That was precisely what I was going to do. Thanks!!!
Noah, these tasks tend to be very parallel and can be spread around different machines via the the network port efficiently.
How ever the RPI is not compute centric... If you want lots of compute for your money go for a simple PC mobo. Almost any basic Mini ITX or whatever will have much more compute than a PI
So if solving the problem is the requirement then doing it with RPIs isnt sensible for most configurations. If creating a cluster to learn from is the aim then go ahead.
Okay thanks!!!