Your confusion is the exact problem my friend had. After some nudging the interviewer rephrased it to be a linked list of finite but unknown length. The issue

Your confusion is the exact problem my friend had. After some nudging the interviewer rephrased it to be a linked list of finite but unknown length. The issue was more that when my friend didn't get it within about a minute the interviewer decided the interview was over and hung up abruptly. If the question is "select a random element from a linked list of finite but unknown length that you can traverse only once" then yes it's at least solvable but I don't think it's a reasonable interview question to demand in less than a minute when the question was additionally ill formed to begin with.