There are 300 students standing in a row. Starting from the first one, they count off in a cycle of 1 to 3. After everyone has finished counting, those who called out multiples of 3 leave the row, and the remaining people move forward to form a new row. This process is repeated until only 3 people are left. What was the initial position of the third person among the last 3 remaining people?
Divide the total number of people by 3, and subtract the quotient from the total to get the difference, which is the total number of people after one operation.
(1) $300 \div 3=100,300-100=200$;
(2) $200 \div 3=66 \cdots \cdots \cdot 2, \quad 200-66=134$;
(3) $134 \div 3=44 \cdots \cdots \cdot 2, \quad 134-44=90$;
(4) $90 \div 3=30, \quad 90-30=60$;
(5) $60 \div 3=20, \quad 60-20=40$;
(6) $40 \div 3=13 \cdots \cdots 1, \quad 40-13=27$;
(7) $27 \div 3=9, \quad 27-9=18$;
(8) $18 \div 3=6, \quad 18-6=12$;
(9) $12 \div 3=4, \quad 12-4=8$
(10) $8 \div 3=2 \cdots \cdots \cdot 2,8-2=6$;
(11) $6 \div 3=2, \quad 6-2=4$;
(12) $4 \div 3=1 \cdots \cdots 1,4-1=3$;

Therefore, after 12 operations, the total number of people decreases from 300 to 3.
Next, we reverse the process from the end, adding 1 person for every 2 people;
(1) Divide the position by 2, if there is a remainder, add the quotient to the position to get the previous position;
(2) Divide the position by 2, if there is no remainder, add the quotient minus 1 to the position to get the previous position;
(1) $3 \div 2=1 \cdots \cdots 1,3+1=4$;
(2) $4 \div 2=2,4+2-1=5$;
(3) $5 \div 2=2 \cdots \cdots 1, \quad 5+2=7$;
(4) $7 \div 2=3 \cdots \cdots 1, \quad 7+3=10$;
(5) $10 \div 2=5, \quad 10+5-1=14$;
(6) $14 \div 2=7, \quad 14+7-1=20$;
(7) $20 \div 2=10, \quad 20+10-1=29$;
(8) $29 \div 2=14 \cdots \cdots 1,29+14=43$;
(9) $43 \div 2=21 \cdots \cdots 1, \quad 43+21=64$;
(10) $64 \div 2=32, \quad 64+32-1=95$;
(11) $95 \div 2=47 \cdots \cdots 1, \quad 95+47=142$;
(12) $142 \div 2=71,142+71-1=212$;

The third person among the final 3 people was initially in the 212th position.