Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

If you had an infinite supply of water and 5-quart and 3-quart pails, how would you measure exactly 4 quarts? What is the least number of steps you need?

Replace the letters of words with a number so that the below equation holds true

BASE +
BALL
---------
GAMES
----------

Sherlock Holmes was challenged to make a pre-drawn line smaller without erasing it. He did it in fractions of seconds. How?

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

A man escapes from jail using help from his girlfriend. The investigators suspect four girls of being the man's girlfriend.

Out of those four girls, one is his girlfriend who is lying. Two of the girls are completely innocent and are speaking the truth. One of the girls is the man's sister who is helping the girlfriend lie. Following are the statements from all four of them:

Ariana: "Myrna is his girlfriend."
Jane: "Angelina is lying."
Angelina: "Ariana is lying."
Myrna: "Jane is not his sister."

Can you find out who is the man's sister among them?

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?

They are three errirs in this question. Can you find them?

One day Jenifer meets the Lion and the Tiger in the Forest of Forgetfulness. She knows that the Lion lies on Mondays, Tuesdays, and Wednesdays, and tells the truth on the other days of the week. The Tiger, on the other hand, lies on Thursdays, Fridays, and Saturdays, but tells the truth on the other days of the week. Now they make the following statements to Jenifer:

Lion: Yesterday was one of my lying days.

Tiger: Yesterday was one of my lying days too.

What day is it?

I went to the bookshop and spent one-half of the money that was in my purse.

When I came out, I found that I had as many cents as I had dollars and half as many dollars as I had cents when I went in. Find the money in my purse when I entered the store.