How are points awarded for solutions eg. in January 13 challenge , someone is given 1 point for a solution and someone less than a point ???

For all exact answer type questions , you get 1.0 points for correct answer and 0.0 for an answer that is not accepted .

Optimization problems which are called CHALLENGE problems here dont have one best answer or rather it is not possible to find the best answer in given time because the problem is NP-Complete or even harder . So there is a scoring policy in such questions which is specified in the problem statement itself . So for example in January contest , the challenge problem is “A Fence for Byteland” . You can see there how scoring is done . The scoring formula for a given challenge problem may not give an answer between 0 and 1 . So the answer with best score ( highest if it is required to maximize score or lowest ( like in January Challenge ) if it is required to minimize score ) is given 1.0 points and everyone else gets a score between 0 and 1 by finding their score’s ratio with the best score .

just an additional information

according to rules it may be called tie break problem

Each contest will have one min/max tie breaker problem, where the best solution will receive one point and all other solutions will receive a fraction based how close they come to the best solution.

This problem is not marked, but you recognize it easily from problem statement, where **scoring** is always described. As described by @vineetpaliwal such score is normalized to be in [0, 1] interval.