Eight of us go fourth, not back, to protect our king from an attack. What are we?

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?

Three doctors said that Bill was their brother. Bill says he has no brothers. How many brothers does Bill actually have?

Can you find the ages of a son, father and grandfather based on the following facts?
The sum of the ages of grandfather, father and son is 140 years.
The age of the son in months is the same as the grandfather in years.
The age of the son in days is the same as the father in weeks.

If in a code language, DISTANCE is written as IDTUBECN and DOCUMENT is written as ODDVNTNE, the how will THURSDAY be coded as in the same language?

What number divided by 4 is the same as that number minus 4?

I have a hole in my back and legs I lack.
I live where I can’t breathe and I eat without teeth.
What am I?

You have two buckets - one holds exactly 5 gallons and the other 3 gallons. How can you measure 4 gallons of water into the 5 gallon bucket?

(Assume you have an unlimited supply of water and that there are no measurement markings of any kind on the buckets.)

There’s a one-story house in which everything is yellow. Yellow walls, yellow doors, yellow furniture. What colour are the stairs?

Christina has four daughters, and each of her daughters has a brother. How many children does Christina have?