Can you find out which number multiplied by itself will give the output as 12345678987654321?

What can run but never walk, have a mouth that never speaks, have a head that never weeps, and have a bed but never sleeps?

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

I know a nine-letter word having only one vowel.
Do you ?

What is next number in the pattern below:

131 517 192 123 ?

A word I know has six letters it contains, remove one letter and 12 remain. What is it?

What is the next number?

77, 49, 36, 18 ?

There are two beautiful yet remote islands in the South Pacific. The Islanders born on one island always tell the truth, and the Islanders from the other island always lie.
You are on one of the islands and meet three Islanders. You ask the first which island they are from in the most appropriate Polynesian tongue, and he indicates that the other two Islanders are from the same island. You ask the second Islander the same question, and he also indicates that the other two Islanders are from the same island.
Can you guess what the third Islander will answer to the same question?

What are the 50th, 63rd and 100th numbers in the sequence below?
4, 5, 8, 8, 9, 9, 12, 13, 13, 13, 17, 18, ...

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?