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Hydra heads brainteaser

By David, 22 April 2021 Brainteaser

Difficulty: Tricky

While out adventuring, Heracles the Hero came across a monstrous, 9-headed Hydra. Without pausing to think, Heracles pulled out his sword and started cutting off the Hydra’s heads.

After several minutes of cutting, Heracles realised it was taking ages to remove the heads. Then he remembered something his friend Euripides told him. Every time you cut off one head, the Hydra grows back two!

Heracles looked at the many-headed Hydra and then the pile of heads he’d cut off. He was going to need a better plan. So he grabbed the decapitated heads and ran away.

Back at home, Heracles counted that he’d cut off 41 heads.

How many heads does the Hydra have?

Scroll down or click for a hint, or the answer!

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Brainteaser hint

If Heracles only cut off one head, how many heads would the Hydra have? What if he cut two? Can you spot a pattern?

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Brainteaser answer

Every time Heracles cuts off one head, two more grow. Writing it out with symbols we get:
– 1 + 2 = + 1
Every time Heracles cuts off a head, the Hydra actually gains one. As the Hydra started with 9 heads, and Heracles cut off 41, the Hydra now has 9 + 41 = 50 heads!

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