Institutional decisions about online education depend on whether difficulties occur separately or accumulate among the same students. This study determines which patterns of concurrent adverse responses are identifiable from survey summaries for two Bangladeshi universities. Twelve item summaries describe 100 students and 30 teachers; the six student margins support a finite-sample analysis conditional on exhaustive binary coding and a common denominator. Integer linear optimization over 64 response patterns yields sharp bounds, while denominator checks and controlled perturbations examine the limits of interpretation. The student margins imply 331 adverse item responses and an average of 3.31 per student. Technical disruption and difficulty balancing academic and personal life must coincide for 47–70 students. At least three adverse responses can occur for 33–100 students, whereas at least four can occur for 11–82. Allowing each margin to change by at most five students widens the latter interval to 1–90. All six teacher agreement percentages fail conventional two-decimal rounding compatibility with unweighted counts out of 30, preventing equivalent count-based inference. The analysis establishes unavoidable overlap between particular difficulties but leaves their overall concentration substantially undetermined. These conditional findings concern the respondent group and do not establish national prevalence, individual support requirements, learning effects, or the effectiveness of any educational intervention.
