Math the Magic

Find the next number in the sequence

5 12 24 36 ?




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If,

6 / 7 = 2
3 / 9 = 7
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Then

4 / 5 = ?

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Which is heavier: a ton of bricks or a ton of feathers?

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The pound is not a finish.

We are sharing a few instructions below, which you have to use in any suitable order to modify the above sentence such that the end sentence is a scientific fact.

- Eliminate a letter and supplement another in its place.
- Take away one word.
- Remove one letter from one word.
- Get rid of two letters from one word.
- Swap a word with its antonym.

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Find the next number in the series?
2, 12, 36, 80, 150, 252, 392, _ ?

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What is the fewest number of coins that would be required in order to make sure each and every coin touches exactly three other coins?

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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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Challenging

There is a cryptic organization called Cicada 3301 that posts challenging puzzles online, possibly to recruit codebreakers and linguists.