Logic Game

Today’s Twister is a follow on to #14 and #15. Venn diagrams is again the theme, but this time you’re given a set and you have to select ALL of the areas of the Venn diagram to which it corresponds. There are two sets, A and B. Each displayed set is a combination of these two sets using Complement, Union or Intersection. It important to realize that one or more areas may be selected, by clicking in the desired area (selected areas are in orange). If you want to deselect an area, just click a selected orange area and it will return to it’s original color. Finally, the blue area can be selected – it corresponds to being outside of both sets A AND B.

“Logic is the beginning of wisdom, not the end.” – Leonard Nimoy

Today’s Twister is a follow on to #14. Venn diagrams is again the theme, but this time it’s with three sets. I have created another interactive game that will help you understand and master Venn Diagrams with three sets. As last time, let’s start by quickly reviewing three set Venn Diagrams. In each puzzle, there will be three big circles (outlined in black). There is a circle on the top left, a circle on the top right and a circle on the bottom. The circle on the left will contain objects of a selected shape – either Circle, Square or Triangle. The circle on the right will contain objects with 0, 1 or 2 holes. The circle to the bottom will contain objects of a selected color – Red, Blue or Green. To the left of the Venn diagram, there are 27 objects. All you have to do is cover each dot in the Venn diagram with a shape. Unlike the last puzzle, there will be a number of shapes left over (exactly 15) and a dot may possibly be correctly covered by multiple shapes.

“A place for everything. Everything in it’s place” – Ben Franklin

Today’s Twister is Venn diagrams with two sets. I have created an interactive game that will help you understand and master Venn Diagrams. First let’s quickly review Venn Diagrams. In each puzzle, there will be two big circles (outlined in black). The circle on the right will contain objects of a selected shape – either Circle, Square or Triangle. The circle to the left will contain objects of a selected color – Red, Blue or Green. At the bottom of the Venn diagram, there are nine objects, 3 circles, 3 squares and 3 triangles. For each shape, there are three colors, so for example there is a red circle, a blue circle and a green circle. All you have to do is place each shape, all nine of them, correctly in the Venn diagram.

Today’s post is something different – Truth Tables. Truth Tables are a great way to learn and master logical statements. That is conditional statements and combining statements with AND (Conjunction) and OR (Disjunction), as well as negating statements. I have developed two new sets of practice problems for truth tables. General statements “p” and “q” are used to represent any statement. Just to review, a statement must be true (T) or false (F). For each problem set, there are four rows (randomly presented in each problem set) and a randomly selected statement. All you have to do is determine the truth value (T or F) of the statement for each row.

As with most of my practice problem sets, perfect practice is imperative. Immediate feedback is provided and this helps you to learn and improve. There are two problem sets below (both interactive). The first does not include any negated statements, so it should help you ease into being successful. The second problem set has everything, AND, OR, Negation and Conditional Statements. All you have to do is to correctly determine the truth values (either TRUE or FALSE) for each statement.

Problem Set 1
AND/OR and Conditional Statements

Problem Set 2
AND/OR/Negation and Conditional Statements

Today’s post was a special request. If you like it, please select the like button below!

“Go fast slowly” – Clarence Stephens

Number Circuits are an original puzzle that I came up with a few years ago.  They are number sense puzzles that require you to arrange a set of numbers in a designated pattern.  I used magic squares as a theme using shapes other than squares. In all, I was able to develop over 200 puzzles all with this same theme.  Fortunately, Mindware liked the puzzles and published two books.  I was pretty excited (and still am).  The books differ in difficulty, although neither set of puzzles are too difficult (although all puzzle are challenging when you can’t solve them!).  Below are four puzzles, two from each book.  I believe they’re representatve of each collection and Number Circuit puzzles in general.  Click each picture to open a full sized pdf image of each puzzle in a new window.

from Number Circuits A	from Number Circuits B

As always, I hope you enjoyed these puzzles. Please pass them onto others who may enjoy them and please click LIKE below if you like them! 

MIndware currently has the books for sale for only $3.95 (that a 69% savings!).  If interested in purchasing either book just click below:

Number Circuits A (Beginner Puzzles)

Number Circuits B (Advanced Puzzles)

“She generally gave herself very good advice, (though she very seldom followed it).” – Lewis Carroll

183 years ago, on January 27th, 1832, Lewis Carroll was born.  Lewis Carroll was just a pen name.  His actual name was Charles Dodgson.   Although he is best known for two books – “Alice’s Adventures in Wonderland” and “Through the Looking-Glass“, he was actually a mathematician at Oxford.  In addition to his writings and math, he loved nonsense.  Nonsense in the form of puzzles, riddles and poems, all of which he loved to develop and pass along to others.

One of his favorite type of puzzles was called a Doublet.  In a Doublet, you start with a word and try to form a second word by changing one letter at a time.  Each time a letter is changed, the new word must be a real word (and not just gibberish).  Here’s an example that changes FLOUR to BREAD

FLOUR
FLOOR
FLOOD
BLOOD
BROOD
BROAD
BREAD

Each new word has just one different letter than the previous word in the list.  Here are four puzzles for you to try in celebration of Lewis Carrol’s birthday.   

1. change SHIP to DOCK
2. change OPEN to GATE
   
3. change CRY to OUT
   
4. change LIES to TRUE
   

These four puzzles are difficult and not necessarily for younger puzzlers.  I hope you enjoy this post. Please pass this onto others who may enjoy it!    Also, click “Like” below if you like it!

“Do not let what you cannot do interfere with what you can do.” – John Wooden

Today’s puzzles are Hex Codes.  Each puzzle is a collection of adjacent hexagons that follow a pattern.  Each hexagon contains either a number/letter or is empty.  The objective is for you to fill in empty hexagons with the correct number/letter that follows the given pattern.  You must determine the pattern that each puzzle exhibits in order to correctly complete each puzzles.  The hexagons may vary in color which may be of importance (hint, hint, nudge, nudge).  Some of the puzzles may use addition or subtraction, while others may utilize some other connection (like adjacent hexagons or the color) between certain attributes.  That’s all for you to figure out. 

So all you need to do is to figure out the pattern in each puzzle and then use it fill in empty hexagons.  Best of luck!


As always, I hope you enjoyed these puzzles.  Please pass them onto others who may enjoy them!

“He who wonders discovers that this in itself is a wonder” – M. C. Escher

Today’s puzzle is an original puzzle which I believe to be very challenging. I call them Self-Referential Puzzles. They are similar to the Number Sense Puzzles (from yesterday) in that you are given a statement for which you find a number. The difference is that in Self-Referential Puzzles, the statement refers to the statements in the puzzles. What’s that mean? Well, in Number Sense Puzzles, statements were something like “Number of quarts in a gallon” which is always 4 (it never changes). In Self-Referential Puzzles, the statement may be something like “The number of even number solutions”. Well this is all together different because when a solution is changed it may impact and change some or even all of the other solutions. 

So, the important thing to remember is that when you enter or change a number in the puzzle it is very likely to effect other numbers.  In turn, the other numbers may change which will likely effect other numbers.  And this goes on and on! That’s the beauty of the puzzle – changing one answer may change all of the answers!

I’ve put together an interactice “drag and drop” puzzle sampler that has six different self-referential puzzles.  As always with my interactive puzzles, you will need to be able to access Adobe Flash.  Each puzzle has it’s own set of directions and numbers that can be used.

“Three things cannot be long hidden: the sun, the moon, and the truth.” – Budda

A counterexample is an example that shows a statement is false. Counterexamples are very important as they can be used to disprove a proposition. For example, given the proposition: “All prime numbers are odd”, 2 serves as a counterexample that disproves the proposition. 2 is a prime number, but it is not odd. It is important to realize that although counterexamples can be used to disprove propositions, examples can not be used to prove propositions.

The Counterexample Game is really straight forward. Given a statement, say whether it’s TRUE or FALSE. If it’s FALSE, then give a counterexample that shows that the proposition is FALSE. What’s great about the Counterexample Game is that it gets you thinking. It’s a great quick game that can be used as a starter for a group (in a classroom environment) or rapid-fire with individuals. The other great feature is that the subject does not have to be math. It can be based on nearly all subjects. Make a statement and if it’s false, just ask for a counterexample.

Below is a five statement counterexample game. Within this game four of the five statements are FALSE, so only one is TRUE (so it doesn’t have a counterexample).

1. All of the state names in the United States contain the letter “e”.

2. All rectangles are squares.

3. All multiples of 3 are odd.

4. All multiples of 2 are even.

5. Connecting three unique dots will always make a triangle.

These statements are from varied subjects (spelling, geometry and arithmetic).  You can gear the statement(s) to the subject matter being reviewed or studied.  Regardless of the subject matter, make it fun.  Challenge the students to think beyond their immediate response.  “I don’t know” is not allowed – encourage thinking.  Reward originality and accomplishment. 

Good luck and have fun.  Please comment if you  like these.  I plan on generating more of these to be used in classrooms.