500 followers problem-2

Logic Level 5

Calvin the Frog is trying to hop across a river. The river has 10 lily pads on it, and he must hop on them in a specific order (the order is unknown to Calvin).

If Calvin hops to the wrong lily pad at any point, he will be thrown back to the wrong side of the river and will have to start over.

Assuming Calvin is infinitely intelligent, what is the minimum number of hops he will need to guarantee reaching the other side?

The answer is 176.

1 solution

A Former Brilliant Member
Feb 24, 2016

Calvin needs (at most) $i(10-i)$ hops to determine the ith lily pad he should jump to, then an additional 11 hops to actually get across the river. Thus he requires $\displaystyle \sum_{i=1}^{10}(i(10-i))+11=\boxed{176}$ hops to guarantee success.

I think it should be the 'maximum number' and not the minimum number of tries.... Correct me please if i am wrong

Yatharth Chowdhury - 5 years, 3 months ago

No it is correct. The question asks minimum number of hops to guarantee reaching the other side. Any number less than it will not guarantee reaching the other side reaching the other side as the worst possible outcome results in 176 hops.

A Former Brilliant Member - 5 years, 3 months ago

Then why is Calvin said to be "infinitely intelligent"???

abc xyz - 5 years, 3 months ago

It takes maximum 9 attempts to know which correct first lily pad. Then 8 attempts (each of 2 hops) for the second one; 7 attempts max (each of 3 hops) for the third, etc. So 1x9 + 2×8 + 3×7 + 4×6 + 5×5 + 6×4 + 7×3 + 8×2 + 9×1 = 165 to know the right path for sure. Then 11 hops to do it = 176. (To my annoyance my own attempt forgot the 11th hop so got it wrong).

Will Hawkes - 5 years, 3 months ago

500 followers problem-2

The answer is 176.

1 solution

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