Category Archives: Logic

Bongard problem colours


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 colours**/*****

You can check your solution 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.

Next month I intend to publish a Christmas special.

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The ancient tablet


1) The ancient tablet**/*****
Some archeologists discovered an ancient tablet. After a concerted effort, the managed to translate four sentences:
Baruntas glizaval kama – the golden crown is hidden
Glu kama valet – the golden bracelet is revealed
Glizaval glu kazu – silver crown is revealed
Baruntas kazu valet – Silver bracelet is hidden

What does “kama valet baruntas” mean?

You can check your solution 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.

If you like this puzzle, you may be interested in my book with similar ouzzles.

Bongard problem 13


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 13**/*****


You can check your solution 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.

Bongard problem 33


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.

Cities



(Illustration: Tiananmen square in Bejing, photo by Nowozin, license GFDL)
Cities****/*****
Have a look at the following cities:
Bejing
Cairo
Istanbul
New York
Sydney
Taunton, Massachusetts

Which of the following three cities also belongs in this group?
a) Amsterdam
b) Berlin
c) London

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.

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 further 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