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http://fantomcoin.org/ allows dual mining.

Their https://bitcointalk.org/index.php?topic=598823.0 page says:

merged mining with Bytecoin (BCN), Monero (XMR), QuazarCoin (QCN), duckNote (duck) or any CN based coin. New blockchain needs no additional hashpower

hmmm... needs no additional hashpower

Question 1: Are the miners hashing fantomcoin's last blocks 'nonce'?

Coinbase says hashing is done by:

"solving a complex mathematical puzzle that is part of the bitcoin program, and including the answer in the block. The puzzle that needs solving is to find a number that, when combined with the data in the block and passed through a hash function, produces a result that is within a certain range. This is much harder than it sounds.

(For trivia lovers, this number is called a "nonce", which is a concatenation of "number used once." In the case of bitcoin, the nonce is an integer between 0 and 4,294,967,296.)

Solving the puzzle

How do they find this number? By guessing at random. The hash function makes it impossible to predict what the output will be. So, miners guess the mystery number and apply the hash function to the combination of that guessed number and the data in the block. The resulting hash has to start with a pre-established number of zeroes. There's no way of knowing which number will work, because two consecutive integers will give wildly varying results. What's more, there may be several nonces that produce the desired result, or there may be none (in which case the miners keep trying, but with a different block configuration)."

Question 2: how can fantomcoin do this with no additional hashpower?

Is fantomcoin just guessing and submitting the same result (for it's own mathematical problem) to other cryptonote networks, hoping that it strikes it lucky!?

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Tari university has a great explanation about what merge mining is here. I strongly recommend you to read it.

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