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POTW is an opportunity to do interesting math problems outside of scheduled math team practices. This is completely optional, and mostly for your personal practice and enjoyment. A problem set is uploaded here every Wednesday afternoon, and you are given a week to do the problems. Each set contains three problems of varying difficulty, usually consisting of an easy problem, a medium problem, and a hard problem. You may submit your solutions to us via email for POTW points. Those who have accrued the most POTW points throughout the year will receive prizes at the end of the year, as well as gain an individual advantage at the end of the year contest. Rules: -Each problem will be marked with an S or a P. S stands for short-answer, meaning you should only submit the answer to that problem, not a full solution. P stands for proof, and these problems require you to give us a full solution to the problem. -Email submissions to vmtpotw0708@gmail.com. Make sure the subject line has the format "POTW_[Week number]_[your name]" For example, POTW_13_Haitao Mao. Unformatted submissions will be filtered out and may not be graded. You may attach scanned handwritten proofs or type them. You may submit your answers and proofs only once per week. Your first submission is your final submission. The strict deadline for submissions is Wednesday at 4:00PM, but it is recommended that you submit them at least the night before. -Make sure to be rigorous! Partial credit may be awarded for the proofs. Each problem will be graded out of seven points. A short-answer problem will be graded based on correctness: right or wrong. Proof problems will be graded on a USAMO scale, meaning that correct solutions will get seven points, correct solutions with minor faults will receive five to six points, corect solutions with major steps missing will receieve three to four, and significant progress will be awarded on or two points. -Calculators and computers can not be used in your proofs. Extremely hideous brute-force proofs are also bad. -You may not submit solutions to problems which you have consulted with other people with(except for clarification purposes). It is fine to discuss the problems, but after doing so, you are on your honor to refrain from submitting anything for the problems you have discussed. Problem Sets: 1 | Problems | Solutions 2 | Problems | Solutions 3 | Problems | Solutions 4 | Problems | Solutions 5 | Problems | Solutions 6 | Problems | Solutions 7 | Problems | Solutions 8 | Problems | Solutions 9 | Problems | Solutions |