1) Lerna's Hydra is a mythological character that appears in some stories such as the 12 Tasks of Hercules. The Hydra was a one-headed monster but when it is cut-off, 2 more heads grow in its place. If a hero tried to conquer it by cutting off all of its heads would the Hydra have on the third day? And at the end of 12 days of trying to kill it?
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512
Step-by-step explanation:
Assuming Hydra's head grows out next day only.
We start with 1 head, it turns 2 next day and keeps on doubling every day.
It will be a geometric progression with common ration (r) = 2 and initial term (a) = 1.
we know,
n-term = ar^(n-1)
So, on 10th day
Number of head = 2^9 = 512