by Bill Graham

Answer to The Meanest Math Teacher from Vol 1, No. 1

If you follow the rules very carefully for several small numbers of students, you'll arrive at a table like the following.

Number of Students	Where You Should Sit
2	2
3	2
4	4
5	4
6	4
7	4
8	8
9	8
10	8
11	8
12	8

You should now have a good clue as to the answer and some insight into why. With each round, the teacher eliminates the odd seating positions of the remaining students. With, for example, 12 students, the first round removes students 1, 3, 5, 7, 9, and 11. The next round eliminates students whose position is double an odd number: 2, 6, and 10. Another round eliminates positions that are four times an odd number: 4 (the only one left). By repeatedly eliminating all odd numbers times increasing powers of two, the teacher ends up with the largest power of two available. The following table provides answers for reasonable numbers of students.

Number of Students	Where You Should Sit
2-3	2
4-7	4
8-15	8
16-31	16
32-63	32
64-127	64
128-255	128