Methods of scoring in multiple choice examinations are outlined in which the examinee's expected change in score because of random guessing must be negative for all situations of partial knowledge. Thus, it can be argued that the guessing component in multiple choice examinations can be completely removed. The examinee is instructed to tick the correct box or, if the correct box is unknown, to cross boxes known to be incorrect, or to leave the question blank. Under the proposed scoring system, it is argued that an examinee will not attempt to demonstrate more knowledge on any particular question than the examinee in fact has. Also, the examiner has quite a degree of freedom as to the size of the rewards for correctly crossed boxes; rewards which need not be equal. There is also quite a range in the possible values of the penalties for incorrect responses and appropriate recommendations are made.