19b Polya's four-step problem-solving strategy

Use Polya's four-step problem-solving strategy and the problem-solving procedures presented in this lesson to solve the following exercise. take place? If eleven people greet each other at a meeting by shaking hands with one another, how many handshakes Part 1 of 2 Each person shakes hands with every other person. Since there are 11 people, each of them shakes hands with 10 10 others. Part 2 of 2 You might incorrectly conclude that there would be a total of 11 - 10 = handshakes. However, counting in this way does not work because each handshake is being counted twice. For example, if two of the people are named Ann and John, the calculation 11 . 10 would count Ann shaking John's hand as one handshake, but it also counts John shaking Ann's hand as another handshake. However, Ann and John shaking hands should only be counted as a single handshake. Therefore, to eliminate repetition we must divide by 2. Thus, the actual number of handshakes that take place is 110 handshakes