The numbers 1 and 12 on the clock face are very familiar things in our daily life, and the numbers on the clock face usually represent hours. Interestingly, however, there is an arrangement that makes the total number of 12 on the clock face equal to 0.

2. Description and analysis of the problem: describe the specific situation of the problem: arrange the numbers of 12 on the clock face so that their sum is equal to 0. Analyze the mathematical properties of the problem: considering that all the 12 numbers on the clock face are integers, we need to find a way to arrange them so that the sum of these integers is 0.

3. Introduce symbols and variables: express the number of 12 as x 1, x2, ..., x 12, and we need to find a solution satisfying the equation x 1+x2+ ... +x 12=0.

4, problem-solving ideas: the characteristics of the arrangement: Because the numbers on the clock face 12 are fixed, it is necessary to consider their arrangement. You can list all possible permutations and combinations in an exhaustive way.

5. Mathematical reasoning and calculation: list and calculate all permutations and combinations by means of mathematical calculation, and check whether their sum is 0.

6. Discovery of mathematical laws: In the process of enumerating permutations and combinations, some laws and special properties may be discovered for further in-depth discussion and analysis.

7. Problem-solving process and results: Enumerating permutations and combinations: Using calculation tools or programming methods, all possible permutations and combinations can be enumerated and their sums can be calculated. Test and result: For each permutation and combination, we test whether their sum is 0. If there is an arrangement that makes the sum zero, we find the solution of the problem.

8. Analyze the characteristics and laws of solution: In the process of solution, we may find some interesting characteristics and laws. For example, a solution with a sum of 0 may have symmetry, or there may be some mathematical model.