Calvin VS Black Dragon
In a game of Dungeons and Dragons, Calvin's character is able to deal damage ranging from 123 to 145 (inclusive) hit points per hit against a black dragon which has 50000 hit points. Assuming that his character always hits, what is the minimum number of hits he must make, in order to ensure that the black dragon is killed ?
The answer is 407.
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1 solution
Observe that ⌊ 1 2 3 5 0 0 0 0 ⌋ = 4 0 6 .
Hence, if he makes 407 hits, he will deal at least 4 0 7 × 1 2 3 > 5 0 0 0 0 damage.
If he makes 406 hits, each dealing damage of 123, then he only does 4 0 6 × 1 2 3 = 4 9 9 3 8 < 5 0 0 0 0 .
Thus, he must hit 407 times to ensure that the black dragon is killed.
Note: For those who think that 345 is the correct answer, note that if Calvin's character does 345 hits at 130 damage each, he does < 4 5 K damage, which is not enough to " ensure that the black dragon is killed".
As an explicit example, if the black dragon has 140 hit points, is 1 hit enough to ensure that the black dragon is killed? Why, or why not?