What do you see in the given picture?

A number with an interesting property:

When I divide it by 2, the remainder is 1.
When I divide it by 3, the remainder is 2.
When I divide it by 4, the remainder is 3.
When I divide it by 5, the remainder is 4.
When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
When I divide it by 8, the remainder is 7.
When I divide it by 9, the remainder is 8.
When I divide it by 10, the remainder is 9.

It's not a small number, but it's not really big, either.
When I looked for a smaller number with this property I couldn't find one.

Can you find it?

I am soft and cuddly that soothe your heart. But, If you pick my last name I am going to tear you all apart. Who am I?

A chess tournament is taking place on knock-out terms (the one who loses the match is out of the game).
(a) If 10 matches are played in total, how many players participated?
(b) If 20 players took part in the tournament, how many matches were played?

Nine marbles are arranged in the image below. Can you slide two marbles to form a square?

There are three houses in a straight row. One is red, one is blue, and one is white. The red house is left of the middle. The blue house is right of the middle. Where's the white house?

How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

What does a man do only once in his lifetime, but women do once a year after they are 29?

What is next number in the pattern below:

131 517 192 123 ?

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not rounded numerals equals 24.