The mention of both Vikings and Greeks indicates that both Norse mythology and Greek mythology are significant to the solution. First it is important to note that the 7 digits of the solution correspond to the 7 days of the week. This is the significance of the Norse mythology references, which tell you where each digit should be placed. Sunday corresponds to the first digit because Sunday is the first day of the week on the calender. So Saturday corresponds to the last digit.

The Greek names refer to planets, which all have Latin counterparts for which the planets are actually named. The planets are then assigned a numerical value based on their order from the Sun. For instance Mercury = Hermes = 1. Here follows a complete list of days and values for the Norse and Greek names, respectively.

Sun = Sunday
Moon = Monday
Tyr = Tuesday
Odin = Wednesday
Thor = Thursday
Freya = Friday
***Saturn/Cronus/Kronos = Saturday***
***Saturday is named for Saturn, which is the Roman name for Kronos, hence the reference to many names depending on whether ou are in Italy or Greece.
you can easily google the full translations/history between modern English days and Old English names

Hermes = Mercury = 1
Aphrodite = Venus = 2
Gaia = Earth = 3
Ares = Mars = 4
Zeus = Jupiter = 5
Kronos = Saturn = 6
Ouranos = Uranus = 7
Poseidon = Neptune = 8
Hades = Pluto = 9

Now, an explanation of each clue specifically. The explantions will go in the order that the clues were given, not the order in which the clues fit into the solution.

1. the Sun refers to Sunday, the first day and so the first digit. Gaia and Ouranous spend energy together, meaning addition. Gaia = 3 and Ouranous = 7. 7+3 = 10. Now remember, only one digit may fit into each spot in the solution. So 10, because it is after 9, is the same as 0, which is why reference to "none remaining" is made.

2. Freya refers to Friday, and so it is the 6th spot in the solution. Aphrodite's vitality is doubled. Because Aphrodite = Venus = 2, then 2 x 2 = 4.

3. The Moon refers to Monday, which is the second spot in the solution. Hades = Pluto = 9, but you must subtract Zeus who works against Hades. Zeus = Jupiter= 5. So 9-5 = 4.

4. Tyr refers to Tuesday, meaning the 3rd spot in the solution. Ares = Mars = 4, which added with Hermes = Mercury = 1, is 4 + 1 = 5.

5. Odin refers to Wednesday he 4th spot in the solution, and Gaia = Earth = 3, plus Ares = Mars = 4, is 3 + 4 = 7.

6. Kronos in this clue refers to both the day of the week and the numeral. Kronos is Saturn, meaning Saturday. Saturn also = 6. No math is done here, which is why Kronos is referred to as standing alone. Because Saturday is the last spot in the solution, it is also mentioned that Kronos is not remembered until very late sometimes.

7. The last clue says Poseidon = Neptune = 8, is detracted from by Zeus = Jupiter = 5, so 8-5 = 3. Thor is mentioned to signal that this digit is or Thursday, the 5th spot in the solution.

Now simply place the mathematical answers in the correct order of the days of the week, beginning with Sunday and ending with Saturday and you get the solution of

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