Whether or not Rimms must be used in pairs depends on 2 things, the Rimms themselves and how many channels are used by your motherboard chipset. The Pentium 4 and Pentium 4 Xeon chipsets (I850 and I860) use dual channel Rdram. That means if your board uses the traditional 16 bit wide Rimms you'll need to install them in pairs. I believe (but I'm not totally sure) the I840 chipset which was used in dual Pentium III systems was also dual channel, so the same would hold true for an I840 dual Pentium III system. The other pentium III Rdram chipsets, (820?) I believe were single channel. On those single channel systems you could of course install single 16 bit wide Rimms. Also, as someone already mentioned, recently 32bit Rimms were introduced. These Rimms can be used on dual channel Rdram system in singles instead of pairs as was required with 16bit Rimms. Of course in order to use those 32bit wide Rimms, you must have a motherboard that is designed for them. That is you couldn't just use a single 32bit Rimm in a dual channle board that's made to accept 16bit Rimms. So basically the answer to the question of whether you must install Rimms in pairs or not is it depends on your particular board.
As for the comments about continuity rimms, that doesn't have anything to do with whether or not you need to install your Rimms in pairs. Anytime you won't be filling all of your Rimm slots with actual Rimms you must install continuity Rimms in the unused slots. This is irregardless of whether or not you have to install the actual Rimms in pairs or not. Their purpose is to terminal the bus. Hence, they are somtimes alternatively reffered to as Terminator Rimms.
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