Calvin VS Black dragon
In a game of Dungeons and Dragons, Calvin's character is able to deal damage of to hit points per hit against a black dragon which has 50000 hit points. Assume that Calvin's character always hits. What is the minimum number of hits that Calvin must make, in order to kill the dragon?
The answer is 345.
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1 solution
Observe that ⌈ 1 4 5 5 0 0 0 0 ⌉ = 3 4 5 .
Hence, if he makes 345 hits, each dealing damage of 145, he will deal 3 4 5 × 1 4 5 > 5 0 0 0 0 damage.
If he only makes 344 hits, even if each deals the maximum damage of 145, then he only does 3 4 4 × 1 4 5 = 4 9 8 8 0 < 5 0 0 0 0 .
Thus, he must hit at least 345 times.