Number Series Puzzle

Find The Next Number in this series.
1, 2, 6, 42, 1806 ?




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I am the first thing you need while camping.
I am always with the person named Marcos Valencia and Carrick.
But Pogba Zlatan and Rooney think I am wasteful and do not need me.
I am the second to the last thing to add when you are making a patch.

What am I?

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What is the last thing you take off before bed?

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There is a unique number which when multiplied by any number from 1 to 6, we will get the new number that contains the same digits only.

Can you find that number?

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There are hundred red gems and hundred blue gems. The blue gems are priceless while the red gems equal wastage. You have two sacks one labeled Heads and the other Tails. You have to distribute the gems as you want in the two sacks. Then a coin will be flipped and you will be asked to pick up a gem randomly from the corresponding sacks.

How will you distribute the gems between the sacks so that the odds of picking a Blue gem are maximum?

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What can run but never walks, has a mouth but never talks, has a head but never weeps, has a bed but never sleeps?

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Assume there are approximately 5,000,000,000 (5 billion) people on Earth. What would you estimate to be the result, if you multiply together the number of fingers on every person's left hand? (For the purposes of this exercise, thumbs count as fingers, for five fingers per hand.) If you cannot estimate the number then try to guess how long the number would be.

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At a party, there are five people and a whole round cake lying at the centre of the table. Only four people will make a cut and take their piece and the last one will get the remaining piece on the table. How can they make sure that everyone gets a 1/5th of the piece?

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A little girl goes to the store and buys one dozen eggs. As she is going home, all but three break. How many eggs are left unbroken?

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If you toss a coin 10 times and it lands heads up every time, what are the chances it will land heads up if you toss it again?

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What is in seasons, seconds, centuries and minutes but not in decades, years or days?

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Amazing Facts

Crossword

The day before the 1996 U.S. presidential election, the NYT Crossword contained the clue “Lead story in tomorrow’s newspaper,” the puzzle was built so that both electoral outcomes were correct answers, requiring 7 other clues to have dual responses.