The paradox of the surprise test

Extract

The announced surprise test has long been a source of puzzlement among laymen and mathematicians alike. On the one hand, it is asserted “There will be exactly one test next week” and, on the other, it is asserted “The day of the test will be a surprise”. Simple logical analysis suggests that these two statements are in contradiction, yet, of course, when the test comes the class is surprised. By 1977, Martin Gardner had published a summary of solutions to the paradox gleaned from over 20 articles in the mathematical and philosophical literature. Most of the views expounded by Gardner admit the contradiction and implicitly invoke the logical rule that asserts that anything whatever can follow from a contradiction. This is also the approach of one of Gardner’s readers who purports to prove that the egg (the paradox of the unexpected egg, hanging, test, etc are all isomorphic) must be in box 5, yet his proof works as well for any other box! Others assume that perhaps the teacher (judge, friend with the eggs) may not be telling the truth, whereas one respondent understands "expected" in the statistical sense of “expected value”.