The thousands digit of a 4-digit number is 4 greater than the hundreds digit. the tens digit is 2 times the thousands digit. the ones digit is one-half the thousands digit. what is the number?

i know it doesn't make sense, why do you think i'm asking, to throw away my well-earned points?

The ones could be a 1, or 2, or 3, or 4, or 5.
The tens is twice the thousands, so it can't be a 10 (cuz that's not a single digit number) and it can't be a 9 (cuz the thousands digit can't be a 4.5) or a 7 (cuz the thousands digit can't be 3.5) and it can't be a 5 or 3 or 1 for the same reasons.  
The tens could be an 8, 6, or 4, or 2.  But if the ones digit is half of something and the tens digit is twice that same number, they could be:
ones:         1               or  2
thousands:2                    4
tens:          4                    8
These are the only two combinations that satisfy all requirements.
And if the thousands digit is 4 greater than the hundreds digit, then the thousands digit can't be 2.
So now do you see?

The american colonies would have been ruled by a king.