# Inception

Algebra Level 4

Leonardo possess a unique power.He can plant an idea in a persons mind through dreams and can extract information from it.So he plans to extract information from multi- billionaire Chinmay to steal his money. Chinmay has kept his whole wealth amounting to $$1729$$ billions in world largest safe which he owns.But this safe has $$50$$ digit combination which is known only to Chinmay. So Leonardo uses his skills to find that combination.

To his surprise finding that combination was much harder than he thought.He found $$1$$st digit in his dream.And $$2$$nd in dream within $$1$$st dream.So he got $$50$$ digits in dream within dreams(chain of $$50$$ dreams).But in first dream $$1$$ minute of real world is equal to $$30$$ minutes in $$1$$st dreams world.And $$1$$ minute of $$1$$st dream's world is equal to $$60$$ minutes of $$2$$nd dream's world.Also $$2$$nd dream's $$1$$ min is equal to $$120$$ minutes of $$3$$rd dream's world and so on following the pattern.

He takes $$10\sqrt { 2 }$$ minutes in $$1$$st dream,$$400$$ minutes in $$2$$nd dream,$$1000\sqrt { 512 }$$ in $$3$$rd dream and so on following a pattern till $$50$$th dream.

So how many minutes of real world he took to find all digits?

Details and Assumptions:

• Take time of that dream taken by Leonardo to find digit in respective dream.

• Time taken by him to find digits and rate of time in dream to real world's time also follow patterns.

• Write answer till 3 decimal places.

• You can use calculator for some lengthy calculations

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