Logic Puzzle

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!

“When you come to a roadblock, take a detour” – Mary Kay Ash

Lateral Thinking puzzles are often referred to as “Thinking Outside the Box” puzzles.  They are similar to riddles in that their solutions are very simple, yet often very difficult to obtain.  Additionaly, Lateral Thinking puzzles are very easily stated.  Believe me, they can be very difficult.  Lateral Thinking puzzles rely on your thinking a certain way, typically the way that does not lead to the solution.

You can ask “yes” or “no” questions (no open ended questions allowed).  Using the answers, you try to narrow in on the solution.  This sounds easy, but most Lateral Thinking puzzles seem contradictory and seem not to have a solution.

I love to solve and make Lateral Thinking puzzles.  Below are two original Lateral Thinking puzzles.  I made a flash program that allows you to select five questions, each of which is accompanied by its answer.  Just click the Question and it will appear.  Good luck with the puzzles and email me your solutions.  I will gladly respond.

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!

Given a number and a two-set Venn diagram, you have to select the area of the Venn diagram where the number should go. Try to place ten numbers as quickly as possible. After each number is correctly placed, a new number and set definitions are displayed. When you’ve completed 10 numbers, you will be told the number correct, the number of misses and the time it took.

Numbers are in the range of 1 to 50 and set definitions include Even Numbers, Odd Numbers, Multiples of 3, 4, 5 or 7, Numbers Less Than 10, Numbers Greater Than 40 and Numbers in the 20’s. So only basic number familiarity is required.

Here’s a quick overview of two-set Venn diagrams (using the diagram below as a reference). There are four areas:

• 1. Not in A and Not in B (this is the blue area)
• 2. In A and In B (this is the yellow area in the middle – the football shape)
• 3. In A and NOT in B (this is the yellow area on the left)
• 4. In B and NOT in A (this is the yellow area on the right)

Just select “Click to Start” to give it a try.  It’s fast paced and can be addictive.  Try to beat your best time and good luck.

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

“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!

“Begin at the beginning and go on till you come the end; then stop.” – Lewis Carroll

Alice returned to wonderland to find that things were very little changed.  She ran into many of her old acquaintances along the way, discovering they too had changed very little.  However, she quickly discovered that her new adventures would have a self-referential twist.

Below are two of Alice’s encounters with the caterpillar.  In the first puzzle, the caterpillar pulls colored and numbered chips from a bag, hiding the numbers from Alice.  He provides Alice (and you) with some details about the numbers and you have to determine what they are.  In the second puzzle, Alice selects numbered cards from a deck which the caterpillar peeks at.  He again provides Alice (and you) with some details about the numbers and you have to determine what the numbers are on each card.  The following puzzles are self-referential – so beware – the numbers may change before your very eyes!

Puzzle 1

The caterpillar held a black bag containing different colored chips. On each chip, there was a number.  From the bag, the caterpillar selected four different color chips:  red, green, blue and yellow.  He looked at the number on each chip and then placed it face down in front of Alice.  Alice saw the color of each of the four chips, but could not see any of the numbers.  The caterpillar noted the following:

The number on the red chip was the number of selected chips with an odd number
The number on the green chip was the number of selected chips with an even number
The number on the blue chip was the number of selected chips with a number greater than 1
The number on the yellow chip was the number of selected chips with a number less than 2

Can you tell the sum of the four numbers on the selected chips?
Can you tell what number was on each chip?

Puzzle 2

Alice selected five cards from a deck of cards and placed them face down in front of the caterpillar. The caterpillar secretly looked at each card. After looking at the fifth card, he smiled and said “very interesting! The cards contain the numbers 1,2,3,4 or 5, either once, more than once or not at all”. He then told Alice the following:

The number on the first card is the number of odd numbers on the selected cards
The number on the second card is sum of the numbers on the first and fifth cards
The number on the third card is a number different than all of the other numbers
The number on the fourth card is the difference of the numbers on the first and fifth cards
The number on the fifth card is the number of even numbers on the selected cards

Can you tell the numbers on each of the selected cards?

I consider these puzzles to be very challenging.  Be patient and go fast slowly.  Here are links to two more self-referetial puzzles #7 (a collection of self-referential puzzles) and #14 (Who Killed Phil M. Mupp).  I am currently generating a book of original self-referential puzzles, all of which have a story behind them (much like the above).  The first chapter is devoted to Alice and her new adventures with self-referential puzzles.  I hope to have the book out early next year.  Click here to look at all of my currently available puzzle books (on Amazon).  Good Luck and pass the puzzles onto others who may enjoy them!

“You don’t have to be a mathematician to have a feel for numbers.” – John Forbes Nash, Jr.

Today’s puzzle is another original puzzle that I’ve named What Goes Where Puzzles.  It’s all about number sense.  For this puzzle, you need to  understand even and odd numbers as well as multiples (of 3 only).  I developed these puzzles to assist children in developing their number sense.

The puzzles are pretty straightforward.  You need to put the numbers 1 through 9 into the empty circles using the hints provided.  It’s important to use the numbers (1 through 9) once and only once.  Once you have filled in each circle with a number from 1 through 9, check by reviewing each hint to ensure your answers match.

Here’s today’s puzzle and good luck!


I love these puzzles, as they develop number sense while encouraging reading, understanding and following directions.  I wrote a book of 100 What Goes Where Puzzles available on Amazon.com – please take a look and pass this onto others. 

Good Luck and pass the puzzles onto others who may enjoy them!

“Eliminate all other factors, and the one that remains must be the truth.” – Sherlock Holmes

Inspector Galois was stumped. He had yet to solve his most recent case, the murder of the wealthy Oil Magnate Phil M. Mupp. There were five suspects in the murder, all of whom seemed to have an airtight alibi. The famous thoroughbred jockey, Horace Racer, was racing at Saratoga. The world famous physician, Karen Rejab, was at her health clinic in Africa. The popular DJ, Mike Refone, was hosting a 24 hour dance marathon in Los Angeles. The real estate mogul, Iva Lott, was closing on properties she recently purchased in Russia. The world famous explorer, Ben Therenbak, was mountain climbing in South America. All had numerous witnesses that eagerly corroborated their whereabouts.

While reviewing the evidence once again, there was a knock at the inspector’s office door. Without looking up, the inspector responded “Come in”. The door opened and entered Junior Inspector Abel. “It’s just the mail sir, only a single letter for you today.” said Abel as he handed the envelope to Galois. Galois took the letter and examined it curiously. It was addressed to Galois, Inspector of Police. Additionally, on the front of the envelope, at the bottom, was neatly printed “Correctly fill in each circle using only the numbers 1 through 5 – Good Luck”. The inspector curiously opened the envelope and removed a single sheet of paper. He unfolded the paper and examined it. Within seconds, he refolded it, looked at Junior Inspector Abel and said “The case is solved. I know the murderer”. The suspect was apprehended and within days the Inspector was proven to be correct. He did indeed know the murderer. What was on the sheet of paper? Look for yourself, it’s replicated below. Can you too solve the case and determine the murderer?

This is an original self-referential puzzle.  To solve the case, complete the puzzle by entering a number (1,2,3,4 or 5) in each circle that correctly matches the clue.  The number in the gray circle will be the murderer.  Remember the nature of self-referential puzzles, when one number is changed, it will likely effect other numbers.  Good Luck and please pass this puzzle and others onto others who may enjoy them!  Also, feel free to select the Facebook Like button below.