Can you find the least possible number such that

If the number is divided by 3, it gives the remainder of 1;
If the number is divided by 4, it gives the remainder of 2;
If the number is divided by 5, it gives the remainder of 3;
If the number is divided by 6, it gives the remainder of 4.

When you stop to look, you can always see me. But if you try to touch me, you can never feel me. Although you walk towards me, I remain the same distance from you. What am I?

See the given image carefully. What you have to do is move the blue checkers in the position of the black checkers and vice versa. You are only allowed to move the checker to an adjacent empty space. Do it in the least possible moves.

I never stop running even when I standstill. If I am formed by joining two identical bodies together, can you guess who I am?

Can you count the number of triangles in the given picture?

_ _ _ IE _ _
_ _ _ IE _
_ _ IE _ _
_ _ IE _
_ _ _ _ IE

Like you see, some letters have gone missing from these words that contain the IE pair at some or the other place. The letters that will be used to fill the blanks are given below. Use them and form meaningful words. Can you do that?

A, C, D, F, H, K, L, M, N, N, O, R, R, S, S, S, T, T, Y and Y.

If you’ve got me, you want to share me; if you share me, you haven’t kept me. What am I?

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?

I sleep during the day and fly at night, but I have no feathers to aid my flight. What am I?

The following question it puts forth you:

25 - 55 + (85 + 65) = ?

Then, you are told that even though you might think it's wrong, the correct answer is actually 5!

Whats your reaction to it? How can this be true?