Online education is important in the COVID-19 pandemic, but online exam at individual homes invites students to cheat in various ways, especially collusion. While physical proctoring is impossible during social distancing, online proctoring is costly, compromises privacy, and can lead to prevailing collusion. Here we develop an optimization-based anti-collusion approach for distanced online testing (DOT) by minimizing the collusion gain, which can be coupled with other techniques for cheating prevention. With prior knowledge of student competences, our DOT technology optimizes sequences of questions and assigns them to students in synchronized time slots, reducing the collusion gain by 2-3 orders of magnitude relative to the conventional exam in which students receive their common questions simultaneously. Our DOT theory allows control of the collusion gain to a sufficiently low level. Our recent final exam in the DOT format has been successful, as evidenced by statistical tests and a post-exam survey.