Slay the Dragon: Defeat 100-Headed Beast with Min. Attacks

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SUMMARY

The discussion centers on a knight's strategy to defeat a dragon with 100 heads using four distinct attack moves: Thrust (5 heads), Slash (15 heads), Chop (17 heads), and Berserk Slash (20 heads). Each attack results in the dragon regrowing heads at varying rates: Thrust (24 heads), Slash (2 heads), Chop (14 heads), and Berserk Slash (17 heads). The knight can only defeat the dragon by executing an attack that precisely matches the number of remaining heads. The objective is to determine the minimum number of attacks required to achieve this goal.

PREREQUISITES
  • Understanding of combinatorial optimization
  • Familiarity with basic arithmetic operations
  • Knowledge of algorithmic problem-solving techniques
  • Ability to analyze and interpret game mechanics
NEXT STEPS
  • Research combinatorial optimization strategies for minimizing attack sequences
  • Explore dynamic programming techniques for similar problem-solving scenarios
  • Study game theory principles related to decision-making in competitive environments
  • Investigate algorithms for calculating minimum paths in weighted graphs
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This discussion is beneficial for game developers, mathematicians, and strategists interested in optimizing attack sequences in gaming scenarios or similar problem-solving contexts.

terripwilliam
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1. Slay the dragon
A knight needs to fight a dragon with 100 heads. The knight has 4 major moves each able to cut off a number of heads: Thrust (5 heads), Slash (15 heads), Chop (17 heads), and Berserk Slash (20 heads). However, for each attack the dragon grows back heads: Thurst (24 heads), Slash (2 heads), Chop (14 heads), and Berserk Slash (17 heads). The dragon can only be killed if the knight uses an attack that cuts of exactly all its remaining heads. (i.e. if the dragon has 10 heads left, it can't be killed in one attack, but if it has 20 it can). What is the minimum number of attacks required to kill the dragon?

2. Strangely Familiar
You are the communications engineer reporting directly to the commander of a communications intercept RVU (Radar Viewing Unit) which scans frequencies for possible enemy information on threats and reconnaissance. You have just intercepted a transmission, but part of it is garbled due to bad weather. The intercept is:
A ? D F ? H J ? L
where ? represents a garbled letter. What are the garbled letters? What advice do you give to your commander?
 
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1. Slay the dragon
11: for instance 5 slashes, 5 chops, finishing it off with a berserk slash
 

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