Optimising Konsistency

Konsistent Karl is taking a specific contest with the following rules:

  1. There are 15 problems.
  2. The \(n\)th problem is worth \(n\) points.
  3. The contest is 15 minutes long.

Karl can solve the first five problems in one minute each, the next five in two minutes each, and the last five in three minutes each. What is the maximum possible score Karl can earn?

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