While nearly every university overbooks each year, relying on sophisticated algorithms that predict just how many admitted students will probably go elsewhere, Iowa officials were stunned to learn this spring how far off they were in their math. This fall’s freshman class is likely to have more than 400 more students than last year’s, an unintended increase of about 10 percent, for a total of just over 4,500.

Though the university considers this a happy accident — much of the growth has come from outside Iowa, including from schools as far away as China and India, whose graduates typically pay triple the tuition of state residents — the looming flood of new students has left the university scrambling to figure out where they will sleep, and how to fit them into some of the most popular courses.