Jana, you see, was a math major and now a famous computer consultant, so she knew exactly what to do.
Jana thanks Lori for his gallantry, and places her plate in the dead-centre of the table. (It's a symmetrical table, so its easy for her to find the centre).
Lori then places his plate somewhere on the table. Jana then oohs and aahs at the cleverness of Lori's placement, then places her plate symmetrically opposite to Lori's (i.e. the same distant from the centre plate as Lori's plate, so that a straight line can be drawn through the centre of her plate, the centre plate, and Lori's plate).
Lori plays again. A bit more oohing and aahing by Jana, and then she again places her plate symmetrically opposite to Lori's.
The cool thing is, as long as Jana continues this pattern, then if there's a place for Lori to place his plate, then there will definitely be a place symmetrically opposite for Jana to play her plate.
Eventually, there will be no place for Lori to play his plate without making an illegal move or having his plate fall to the floor...
Maybe if Lori woke up a little earlier in the morning, he would have known not to offer to let Jana go first!
