Can you find a number that lies one third of the distance between 1/3 and 2/3?

I welcome the day with a show of light, I stealthily came here in the night. I bathe the earthy stuff at dawn, But by noon, alas! I'm gone.

If you read clockwise, you can form a word by inserting three missing letters in the picture given below. Can you do it?

An equation has been laid down using a few matchsticks. However, as you can see, the equation is not correct. Can you correct the equation if you are allowed to add or remove 5 matchsticks?

The Little ant seems to be always confused. Do you know why?

You have four chains. Each chain has three links in it. Although it is difficult to cut the links, you wish to make a single loop with all 12 links. What is the fewest number of cuts you must make to accomplish this task?

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.

They came out at night, without being called.
They lost at day, without being stolen.
Who are they?

Can you solve the maths in the below-given picture equation?

A woman named Maria was at the funeral of her mother. She met a nice young man that she had never seen before and after the service, they spent a bit of time together. Then she got busy and didn’t get his name or phone number before he left. She tried to find him, but no one knew who he was or how to contact him. A few weeks later, Maria’s older sister dies and the police suspect murder. Who killed the sister?