Category Archives: Logic

Truth-speakers, Liars and Switchers



The remote island of Zwrazr in the Logico archipelago is inhabited by three types of people: Truth-speakers, Liars, and Switchers. Truth-speakers always speak the truth, Liars always lie, and Switchers alternate their sentences between a true sentence and a lie.

As you arrive on the island, a group of three natives comes to greet you. According to tradition, the group consist of one representative of each group. Luckily for you, they introduce themselves:

  • The left one says: I am a truth speaker
  • The middle one says: I am a liar
  • The one on the right says: I am a switcher

So now you know who is who, don’t you?

You can check your solutions here

New puzzles are published at least twice a month on Fridays. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars.

On the isle of Uauau



On the isle of Uauau the natives speak the truth on one day and lie on the next. On his or her “truth-day”, the man or woman will always speak the truth, and on their “lie-days” they will always lie. As a furthttps://justpuzzles.wordpress.com/?p=5097&preview=trueher complication, their truth days and lie-days are not synchronized, what is a truth day for one of them can be a lie day for his neighbor, father, brother or friend.

1) Today is a truth-day for me*/*****
You meet a native who says: “Today is my truth day”. Can you conclude if he has a truth-day or not?

You can check your solutions here

2) Yesterday*/*****
On Friday you meet a native who tells you: “Thursday is one of my lie-days”. Can you conclude if the native is speaking the truth or not?

You can check your solutions here

3) Different truth-days**/*****
You meet two natives. One of them tells you:
“My friend and I have different Truth-days. Today is my friend’s lie-day.”
Does at least one of them have a lie-day?

You can check your solutions here

4) Friday(1)***/*****
You meet two natives, let’s call them A and B as their real names are hard to pronounce. A says:
(1) My friend and I have the same truth-days.
(2) Last Friday my friend had a lie-day.
Does A speak the truth?

You can check your solutions here

5) Friday(2)***/*****
You meet two natives on a Friday. For a change, let’s call them A and B, as their names are hard to remember. A says:
Yesterday I would have said that Friday is B’s truth-day.
Does B have a truth-day today?

You can check your solutions here

What comes next?


what comes next?****/*****
1, 1, 2, 5, 12, 35, 108, …

You can check both your solutions here

New puzzles are published at least twice a month on Friday. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars.

Bongard problem 34


The Russian scientist M.M. Bongard published a book in 1967 that contains 100 problems. Each problem consists of 12 small boxes: six boxes on the left and six on the right. Each of the six boxes on the left conform to a certain rule. Each and every box on the right contradicts this rule. Your task, of course, is to figure out the rule.

Bongard problem 34**/*****


You can check your solutions here

You can find more Bongard problems here and at Harry Foundalis site, and in the category ‘Bongard problems’ in the right margin of this page.

New puzzles are published at least twice a month on Fridays. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars.

Logigram – the meeting


In the small village of Traspass-upon-sea, actually some 50 miles from the nearest sea, the four shopkeepers, mr. Baker, mr. Butcher, mr Grocer and mr. Smith held their yearly meeting on the promotion of Tourism.
Of these four men, only mr Butcher’s trade corresponded with his name.
At the meeting, the grocer was the secretary.
James presided the meeting.
Jesse Smith is not the baker.
The treasurer, mr. Grocer, is not called John.
Neither John nor Jack is butcher.
Who was vice president of the meeting? Who is the smith of the village?

You can get a hint

What’s next?


What comes next?****/*****

1,000, 1,000,000,000, 20, 100, 1, 4, 8, 3, ?

You can check your solutions here

New puzzles are published at least twice a month on Friday. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars.

This puzzle is a free translation of an AIVD (Dutch sister of NSA) puzzle in 2012.

Flags of countries (2)


Flags of countries (2)**/*****
178px-flag_of_el_salvador-svg
200px-flag_of_australia-svg
200px-flag_of_honduras-svg
flag_of_argentina-svg
flag_of_armenia-svg
flag_of_botswana-svg
flag_of_estonia-svg
flag_of_guatemala-svg
flag_of_israel-svg
flag_of_the_czech_republic-svg
flag_of_the_netherlands-svg

Which of the following three flags belongs to the group above:
flag_of_monaco-svg
flag_of_norway-svg
flag_of_sudan-svg

You can check your solutions here

New puzzles are published at least twice a month on Friday. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars.

Flags (1)


Flags of countries (1)***/*****
Look at these flags:
flag_of_belgium-svg
flag_of_the_peoples_republic_of_china-svg
flag_of_colombia-svg
flag_of_germany-svg
flag_of_hungary-svg
flag_of_lebanon-svg
flag_of_mali-svg
flag_of_romania-svg
flag_of_serbia-svg
flag_of_slovakia-svg

Which of the following three flags belongs in the above group:
a) 200px-flag_of_slovenia-svg
flag_of_guinea-bissau-svg
flag_of_bulgaria-svg

You can check your solutions here

New puzzles are published at least twice a month on Friday. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars.

Christmas puzzle


The Dutch equivalent of the CIA & NSA is called the AIVD. One of their departments has been compiling a set of Christmas puzzles for decades, and since a few years these puzzles are published on the internet. You can download the 2016 version.

Though most puzzles are language dependent (in Dutch), there are some which at least on the surface do not seem to require knowledge of the Dutch language.
Here is a list of the exercises and the translation of the exercises/hints of the puzzles for which you probably don’t need to know dutch:
2. Elementary: Which one is out of order?
4. What is the next number in each of the two series?
10. Two persons on a ferry are comparing two rows. One counts differences, the other comparisons. They arrive at the following series. What are the next numbers?
23. Sequences. What are the next three items in the lists?
I warn you, they have the reputation to be pretty tough. 100 points can be earned each year. Every year, people crack all exercises, but in no year did one person all problems.

Thanks to our daughter Joella, who solved puzzle 1b, I can offer you the puzzle below. Which number should replace the question mark:
?
position
drawback
frazzled
bragging
phishing
eternity
sickness

No, I don’t intend to publish the solutions. But I guess the solutions will be published here

How many?


2000px-Searchtool.svg
1) The logicians club**/*****
Yesterday I visited a club of logicians. It’s a very special club, only trained logicians are admitted as members. During the club meetings, all members are required to speak the truth the entire evening, or to lie the entire evening. All members were seated around the circular table, truth tellers and liars alternating. I was not a member and watched from a distance. The president of the club welcomed all the members, and especially me as a guest.
He also explained some more rules which I admit I have quite forgotten. One part of the evening consisted of questions the members asked about the rules, while another topic were the finances.
At the end of the meeting, I asked the president how many members this club had. He happily told me that all 20 members had been present. When I was about to leave, I suddenly realized that the president himself need be trusted, and asked the secretary if the president had spoken the truth.
“Oh no!” the secretary exclaimed. “You should not believe the president, tonight he was a notorious liar! At this evening’s meeting, all 21 members were present!”

Whom should I believe? And why?

The puzzle above comes from “Denken als Spiel”, by Ernst Hochkeppel, one of the earliest puzzle books I obtained.

You can check your solutions here

2) The party***/*****
Once there was a party where everybody with 100 people. Everybody shook hands with a number (some or all) of other people. Everybody present was either a liar (someone who always lies) or a Truthteller (someone who always speaks the truth).
When leaving the party, everybody was asked with how many Truthtellers he or she had shaken hands with. All answers 0, 1, 2, etc till 99 occurred exactly once.

How many Truthtellers were at the party?
This puzzle can also be watched as a video by Mindyourdecisions on youtube.

You can check your solutions here

New puzzles are published at least twice a month on Friday. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to three stars.