I was reading In Code by Saray Flannery,one of the problem in the book bothered me, it is not the problem itself, it is the solution. A Party Trick If someone tells me 2, 2 and 3 are the remainders when she divides her age by 3, 5 and 7 respectively then I can work out her age. Solution: Let x = 2, y = 2, z = 3 and a = the age of the girl. Then she used this formula: a = (70x + 21y + 15z)mod n = (120 + 42 + 45)mod (3 x 5 x 7) = 227mod105 = 17 years old I have no idea of how this works. Where does this formula come from? There must be a logical way to explain this right? And are there any other ways of solving this kind of problem?