This problem seems simple, but it needs some mathematical thinking and skills. Let's look at the solution to this problem.
Solution 1: reverse thinking method
This method is ingenious. It started from the seventh day and got the answer backwards. The specific operation steps are as follows:
1. There is only one liter of oil left on the seventh day, so the oil quantity on the sixth day is (1+ 1)×2=4 liters;
2. Similarly, the oil quantity on the fifth day is (4+1) × 2 =10l;
3. On the fourth day, the oil quantity is (10+ 1)×2=22 liters;
4. On the third day, the oil quantity was (22+ 1)×2=46 liters;
5. The oil quantity on the second day is (46+ 1)×2=94 liters;
6. The oil quantity on the first day is (94+ 1) × 2 = 190L.
So, at first, the capacity of this barrel of oil was 190 liters.
Solution 2: Algebraic Operation
This method is relatively straightforward, and the problem is solved by algebraic operation. The specific operation steps are as follows:
1. Suppose this barrel of oil has x liters at the beginning;
2. Add one liter to the half sold on the first day, and the remaining oil amount is (x-(x/2+1)) = (x/2-1) liter;
3. After selling the remaining half, add one liter the next day, and the remaining oil amount is ((x/2-1)-((x/2-1)/2+1)) = (x/4-3/2) liter;
4. Similarly, on the third day, the oil quantity is (x/8-7/4) liter, on the fourth day, it is (x/ 16- 15/8) liter, and so on, and on the seventh day, it is 1 liter;
5. Therefore, we can list the equation: x/64-63/64= 1, and the solution is x= 190.
So, at first, the capacity of this barrel of oil was 190 liters.