What's the only room from which no one can enter or leave

Find the next number in the series.
1 10 24 43 67 ?

Find out a multi-digit number that if multiplied by the number 9 or any of its multiplications products (i.e. 18, 27, 36, 45,..) will result in the multiplication factor repeated (n) number of times.

In the below-given picture of a pretty girl, there is something wrong. Can you find out what it is?

Find the Odd One Out?
84129
32418
47632
36119
67626
72927

Which is the smallest number that you can write using all the vowels exactly once?

What is the four-digit number in which the first digit is one-third the second, the third is the sum of the first two, and the last is three times the second?

You need to complete the maze by entering from the entrance marked below in the figure near the yellow circle, bottom left and leaving from the exit point near the green circle, bottom middle.

Rule of Game: You can move only by exchanging green and yellow circles.

Can you find out a way through which you can make five squares out of the given figure by moving just six match sticks?

I have a clock(12-hour format) and both the needles of the clock overlap at 12:00.
After how much time, they will overlap again?