Rubix Cube Corner Flipping

[Sidney johnson]

For those who haven't used a rubix cube there are certain patterns you simply cannot achieve, for example if you flip exactly 1 corner to the right or left, either by taking it out or by simply twisting it you can not solve it without either twisting it back or twisting all other corners relative to it, or you can turn all but one other corner in different directions and then be able to solve it. Or you can turn all of the corners and try to solve it and you will only have one corner turned wrong. I can not figure out the math behind this. Can someone explain if you can.