People who do well at programming contests generally have above-average problem solving skills. It is the presence of these skills which drives companies such as Google to place high value on people who excel at programming contests.
These problem solving skills are useful in grad school as well. Many projects involve some level of problem solving. Other projects require a lot of optimization, which is again something that people who do programming contests excel in.
As mentioned in Brian Bi's answer to Do red coders and targets read the full question in a SRM?, people who do programming contests are skillful at cutting away at the verbiage surrounding a problem and getting to the bare-bone description required to solve the problem. This skill comes in handy in several other situations as well.
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Vijay Chidambaram on Quora:
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