Logical Strategy: Casework — Practice problem

Trillian and three of her friends separately arrived at a Restaurant at the End of the Universe, each one minute apart. None of them noted their time of arrival and each of them forgot what time their reservation was for. In the next three minutes, the three members of another party arrived separately, exactly one minute apart, for their 7:00 p.m. reservation at Table 3. Sometime during these seven minutes in which people were arriving, the clock struck 7:00 p.m.

Trillian looked at the empty reserved tables in the restaurant trying to figure out which one was the correct reservation. There was Table 1 for a party of one at 7:00 p.m., Table 2 for a party of two at 6:45 p.m., and Table 4 for a party of four at 7:15 p.m.

Since Trillian is a brilliant mathematician and astrophysicist, her alien friend Zaphod Beeblebrox explains the principles of "bistromath", in the hopes that she can deduce something about their reservation. Quoting from the Douglas Adams novel Life, the Universe and Everything:

"Bistromathics itself is simply a revolutionary new way of understanding the behavior of numbers. Just as Albert Einstein's general relativity theory observed that space was not an absolute but depended on the observer's movement in space, and that time was not an absolute, but depended on the observer's movement in time, so it is now realized that numbers are not absolute, but depend on the observer's movement in restaurants.

The first nonabsolute number is the number of people for whom the table is reserved. This will vary during the course of the first three telephone calls to the restaurant, and then bear no apparent relation to the number of people who actually turn up.

The second nonabsolute number is the given time of arrival, which is known to be one of those most bizarre mathematical concepts, a recipriversexcluson, a number whose existence can only be defined as being anything other than itself. In other words, the given time of arrival is the one moment of time at which it is impossible that any member of the party will arrive."