Find the Next No.

Look at this sequence from top to bottom. What is the next number in the sequence?
1
11
21
1211
111221
312211




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Our product and our sum always give the same answer. Who are we?

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Replace all '*' with digits 1, 2, 3, 4, 5 and 6 to make below statement true.

* *
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I have two coins.
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We have arranged an array of numbers below. What you have to do is use any kind of mathematical symbol you know excluding any symbol that contains a number like cube root. You can use any amount of symbols but you have to come up with a valid equation for all of them.

0 0 0 = 6
1 1 1 = 6
2 + 2 + 2 = 6
3 3 3 = 6
4 4 4 = 6
5 5 5 = 6
6 6 6 = 6
7 7 7 = 6
8 8 8 = 6
9 9 9 = 6

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Chocolate costs 6 rupees and a Toy costs 5 rupees. If you have 32 rupees in total, how many chocolates and how many Toys can be purchased with that amount?

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A rain drop fell from one leaf to another leaf and lost 1/4th of its volume. It then fell to another leaf and lost 1/5th of the volume. It again fell on another leaf and lost 1/5th of the volume.



This process kept repeating till it fell on the last leaf losing 1/75th of its volume.



Can you calculate the total percentage of loss from the initial volume when the drop has fallen to the last leaf accurate up to two decimal places?

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Can you solve below mathematical equation?

2^1234 - 2^1233

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Amazing Facts

Word ladder puzzle

The word ladder puzzle was invented by Lewis Carroll, author of Alice’s Adventures in Wonderland.