Download presentation

Presentation is loading. Please wait.

Published byTamia Dore Modified over 2 years ago

1
Handshake Problem and Phone Call Problem Handshake Problem a)If there are 30 people in a room and everyone has to shake hands, how many handshakes will there be? b)What about if there are n people in the room? Phone Call Problem a)30 people are invited to a party. If every person speaks to every other person on the phone beforehand, how many phone calls will there be? b)What about if there are n people invited to the party?

2
Student 1 ViewPoint – Start Simple! Number of People 12345 Number of Phone Calls 1 person 4 people 5 people 2 people 3 people 013610

3
Sequence: 0, 1, 3, 6, 10, 15,... +1+2+3+4+5 +1 Since the second difference is constant, we have a quadratic sequence with first term ½ n² Compare Original Sequence with½ n² -0.5, -1, -1.5, -2, -2.5, -3,... T(n) = -½n Therefore T(n) = ½ n² - ½n Sequence: 0, 1, 3, 6, 10, 15,... ½ n²: 0.5 2 4.5 8 12.5 18

4
Questions you might ask yourself? 1)What do T(n) and n represent? 2) Does the formula work?

5
Student 2 Viewpoint Start with less people. For example when n = 6 If there are 6 people then every single person will have to make 5 phone calls. 6 x 5 = 30 calls However, this is twice as many calls as is needed because if you´ve already been called by someone then you don´t need to call them back. Therefore, the number of calls is: 6 x 5 = 15 calls 2

6
Student 2 Viewpoint Hence for n = 7 people, the number of calls is: 7 x 6 = 21 calls 2 For n = 8 people, 8 x 7 = 28 calls 2 For n people, n x (n-1) = Number of calls 2

7
Student 2 Viewpoint (without words) 6 x 5 = 30 calls 6 x 5 = 15 calls 2 7 x 6 = 21 calls 2 8 x 7 = 28 calls 2 n x (n-1) = Number of calls 2 Which is easier to understand?

8
Student 3 viewpoint Number of Telephone Calls = What does this mean? Out of n objects, how many ways are there to choose 2 of them? E.g. If you have one object: can´t choose two of them! two objects: 1 way to choose three objects: 3 ways to choose four objects: 6 ways to choose five objects: 10 ways to choose etc. Lisa & Bart Lisa & Homer Bart & Homer Lisa & Marge Bart & Marge Marge & Homer Lisa & Maggie Bart & Maggie Marge & Maggie Homer & Maggie So we do have the triangle number sequence again: 1, 3, 6, 10, 15,...

9
Why does = n(n-1) ? 2 = n! 2!(n-2)! = n x ( n-1) x (n - 2)! 2! (n – 2)! = n(n – 1) 2 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1

Similar presentations

OK

“The Handshake Problem” Problem Solving Ch 1. Shake Hands with Everyone Some things to think about: How many handshakes occurred? How did you keep track.

“The Handshake Problem” Problem Solving Ch 1. Shake Hands with Everyone Some things to think about: How many handshakes occurred? How did you keep track.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on mental health act 1987 Gyno appt on period Ppt on vision and mission of infosys Ppt on poverty and hunger in india Ppt on culture and science in the ancient period Ppt on event driven programming code Best app for viewing ppt on ipad Ppt on commercial use of microorganisms Ppt on area of parallelogram games Ppt on advanced energy conversion systems