Section 7

It is all quite Logical! - Not

 

The deep end is a very good end to start with logic!


Task 1

There are three boxes and the labels on them are all incorrect. One box say  it contains only white socks. Another box says it contains only black socks. The third box says it contains a mixture of block socks and white socks.
Your task is to choose one sock from one box and relabel the boxes so they are all correct.


            Logic Puzz1
                                        These labels are all wrong!

 

At first this problem seems crazy. The solution is quite logical! The box called black and White is wrong, as all the labels are wrong, so it must be either Black or White. Taking a sock from this box determines what label it should have. The simply swap teh other labels and all are correct!


Logic is about true and false. A cat is black or not black. It is one or the other, not both.

 

Logic is about IF -THEN and NOT.


The IF-THEN logic is used a lot. For example "IF" I say two angles in a triangle add to 125 degrees "THEN" the other angle must be 180-125 or 55 degrees. These logical statements use a lot of other connected knowledge. In this problem we also know that there are only three angles in a triangle, and that these three add to a total of 180. All of this is recorded in a structured way.


Logic 2
                problem
One way to record the logic

 

Task 2
Another triangle has all the angles the same size. Draw the triangle. What is the size of each angle?


Logic problems can be in words as well.


Task 3
Five people were eating apples, A finished before B, but behind C. D finished before E, but behind B. What was the finishing order?


and can be amazingly complex. 


The following version of the puzzle appeared in Life International in 1962:



There some very cool ways to "draw" or "image" logic.

A flow chart is a structure that lists the logical steps for a procedure to be completed. The procedure is a called an algorithm. When we add two numbers like 367 + 863 we would probably use the algorithm that is often taught in schools or find the 21stC algorithm called a calculator. The calculator contains many different logical procedures that generate answers to requests like "What is Sine(36)" or "What is 3.45 squared".

Here is a flow chart that describes the process of "Looking for Something". It is a bit simple but contains some good information. The "Start' box is a rounded rectangle and the "End" is teh same shape. A "Statement" is a rectangle. A Decision box is a rombus shape with a Yes or No choice of direction. These boxes are joined by lines with arrows.

Simple Logic
          flowchart
Task 4
Draw a flowchart for one of these.
    (a) Making breakfast.
    (b) Getting dressed in the morning.
    (c) Multiplying two three digit numbers (like 234 x 123).

Here is a website with a course in logical deduction. https://brilliant.org/courses/logic-deduction/ It is free but you do have to sign in with an email address.

This website has a heap of cool problems in logic. https://www.transum.org/Software/SW/Starter_of_the_day/Similar.asp?ID_Topic=21

To finish here is reminder about the popular game called Mastermind.
Mastermind Picture
Of course there are now online versions! https://www.webgamesonline.com/mastermind/
Task 5
Play a game!

Venn Diagrams are very visual ways to "see" logic. The diagram below shows two circles or "sets" A and B. The overlap. What has been shaded is what is not in A or A'. The superscript "dash" means not. The curly E is the Universal set.

For example E might represent the set of all animals. If A is the set of all animals called cats then the shaded part is all animals that are not cats. Both tigers and dogs have places to be. What could Set B contain?
Venn diagram
Venn Diagram show A' or what is Not in A

A grid can be used to solve logic problems as well. This problem comes from a book called Brain Benders. Each clue is recorded with a tick or a cross. Note that of a box has a tick the rest of the boxes in that row and column have X's. making up the grid requires some thought, especially with multiple options.

Task 6
Complete the grid and figure out the who goes by what transport.

Grid puzzle


Computer programs are logical based and a programme like Excel can be used to practice your skills.

Task 7
Write a statement that decides if a number is odd or even.


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Well done, four sections over! On to Section 7! Is the course fun? Use the Navigator to find the next section.