One problem with this is that "surprise" seems to be used in two rather incompatible ways — Terrapin Station
If we take that approach then the statement of the judge is false because whatever day it occurs, the prisoner will be able to prove it must happen on that day, because the system is inconsistent. Here's why:Yes, it is a poor choice of word.
Rather than:
'the hanging will be a surprise to the prisoner'
Better to say:
'prisoner will not be able to deduce the time of hanging' — Devans99
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