How many CryptoNote based currencies exist today?
Have ring signatures appeared in any cryptocurrencies that are not based on CryptoNote?
How many CryptoNote coins are not using a CryptoNight based PoW?
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There's less than a couple dozen CN based currencies. See http://mapofcoins.com/bytecoin.
Shadowcash tried to implement ring signatures on a Bitcoin code base. See https://shnoe.wordpress.com/2016/02/11/de-anonymizing-shadowcash-and-oz-coin/.
To my knowledge, no non-CN coin uses Cryptonight. -- Oops, I misread that last question, see lethos3's answer to that one below.
CryptoNote coins that do not use standard CryptoNight:
Boolberry - Uses
Wild Keccak instead of CryptoNight;
Pebblecoin - Used a POW algorithm named
Boulderhash in the POW mining phase, it required 13 GB of RAM to mine but it has since switched to DPOS;
AEON - Uses a modified Cryptonight algo named