Selling oil Weng is a classic arithmetic problem, and it is also a common problem in middle school students' mathematics competitions. It means: a person who sells oil has a barrel of oil. On the first day, he sold half a liter, the next day he sold the remaining half a liter, the third day he sold the remaining half a liter, and so on. On the seventh day, there was only one liter of oil left. How many liters was this barrel of oil at first?

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.