Because, suppose four people are: A, B, C and D, and A has to shake hands with B, C and D once, and * * * needs to shake hands three times. When Party B shakes hands, since Party A has already shaken hands with Party B once, there is no need to shake hands again, so Party B should shake hands with Party C and Party D once and twice. When C shakes hands, C only needs to shake hands with D once because C has already shaken hands with A and B, and there is no need to shake hands again. Ding no longer needs to shake hands. They have to shake hands six times at a time, so the answer is: six times.
Mathematical handshake problem is a typical combination problem, which is often used to discuss the number of handshakes between people. Suppose there are n people together, everyone has to shake hands with others once and can't repeat it. We can use combinatorial mathematics to solve this problem.
N people shake hands with others once, and everyone will have (n- 1) chances to shake hands (because they can't shake hands with themselves). But because every handshake will be counted twice, it needs to be divided by 2 to eliminate double counting. Therefore, when there are n people together, the total number of handshakes can be expressed by the following formula:
Handshake = (n * (n- 1))/2.
Skills of solving combinatorial problems
1. Understand the basic principle of combinatorial mathematics: Combinatorial mathematics involves the concept of permutation and combination. Arrangement is the choice of considering order, and combination is the choice of not considering order.
2. Use permutation and combination formula: permutation and combination problems can usually be calculated by permutation formula (such as nPr) and combination formula (such as nCr). These formulas can help you determine the number of possible choices and permutations.
3. Pay attention to the situation of repetition and non-repetition: in some problems, there may be choices of repetition and non-repetition. According to the specific situation of specific analysis, consider how to calculate.
4. Using addition principle and multiplication principle: addition principle is suitable for the combination of multiple independent situations, and the multiplication principle is suitable for the multiplication of multiple steps or conditions. Apply these principles flexibly according to the requirements of the problem.
5. Use reverse thinking: Sometimes, considering the opposite situation of the problem will make it easier to solve the combination problem. For example, if it is difficult to calculate the number of combinations that meet a certain condition, you can calculate the number of combinations that do not meet the condition, and then get the result through subtraction.
6. Break down a big problem into small problems: Sometimes, a big problem can be solved by breaking it down into smaller sub-problems. Consider how to decompose the problem into more manageable sub-problems.
7. Practical operation and practice: Mastering combinatorial mathematics requires practice and practice. Try to solve various combination problems and be familiar with different skills and strategies.