What can you catch but never throw?

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

It's a 7-letter word.
If we remove 1 letter from it, it remains the same.
If we remove 2 letters from it, it remains the same.
If we remove 3 letters from it, it remains the same.
If we remove all the letters from it, still it remains the same.
What is it?

You have a roll of cloth 1km long. You have a machine which cuts this roll into pieces of 10-meter-long cloth.

How long would it take for the machine to cut the roll if each cut took 4 secs?

Replace the (?) with the correct mathematical signs to make the expression equal to 59.

18 ? 12 ? 4 ? 5 = 59

In a contest, four fruits (an apple, a banana, an orange, and a pear) have been placed in four closed boxes (one fruit per box). People may guess which fruit is in which box. 123 people participate in the contest. When the boxes are opened, it turns out that 43 people have guessed none of the fruits correctly, 39 people have guessed one fruit correctly, and 31 people have guessed two fruits correctly.
How many people have guessed three fruits correctly, and how many people have guessed four fruits correctly

What is the relationship between these matchstick pictures below?

Identify the next two numbers in this series.

101, 112, 131, 415, 161, 718, ???, ???

Cristina leaves home and then she makes exactly 3 left turns and returns home where she found 2 girls wearing the mask.

Who are these two masked girls?

How can you make the following equation true by drawing only one straight line: 5+5+5=550 ?