# Dragons and Dragon Slayers

• In the Kingdom, there are 7 dragons and 7 dragon slayers.

• Each dragon has ($$\text{index}\times10000$$) hit points (i.e. $$10,000\to70,000$$).

• Each dragon slayer does ($$\text{index}\times1000$$) damage (i.e. $$1,000\to7,000$$).

• The local King asks the dragon slayers to slay all the dragons.

• Each slay round consists of each dragon slayer each attacking a single dragon.

• A dragon slayer cannot attack the same dragon again until he has attacked all remaining dragons.

• Dragon slayers don't die.

• The King figures it will take them at least $$10$$ slay rounds (hit point to damage ratio), and offers to pay $$2,000,000-(\text{number of slay rounds taken}\times100,000)$$.

Can it be done?

• After a slayer attacks each dragon once, may it attack the same dragon 3 times, or must it attack a different dragon each of the last 3 rounds? – noedne Apr 18 at 4:11
• @noedne; it's in rotation, so abcdefgac isn't allowed unless b has died in the process. – JMP Apr 18 at 4:13
• Can slayers attack the same dragon in the same round? – noedne Apr 18 at 4:14
• @noedne; yes, excess damage is wiped out though – JMP Apr 18 at 4:16

Yes, it can be done.

Each round, every slayer attacks for a total of 28,000 damage. So,

If we first reduce player damage by 1000, then it will be easier. I have come up with this table:

Rounds 10000 20000 30000 40000 50000 60000 70000
1 1,3,6 2 7,5 4
2 2,3,4,5 7,6,1
3 2,3,4,5,6 7,1
4 2 1,3,5,6,7 4
5 7 1,4,6 2 3,5
6 1,4,5,6 3,7 2
7 2,3 5 6 4 1,7
8 1,2,3,4,5,7 6
9 1,2,3,5,6,7 4
10 4 1,2,3,5,6,7