Category Archives: Logic

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.

On the isle of Odders and Eveners (1)


2000px-Searchtool.svg
Which day of the week is it?**/*****
Inspector Simon Mart opened his eyes. The lights hurt and he quickly closed them again. Slowly his memories returned. He had landed on the island of Odders and Eveners in the Logico archipelago. Like all islands in this archipelago, the inhabitants had strange habits when it came to speaking the truth and when lying.
The Odders spoke the truth on the odd days of the week: On Sunday, Tuesday, Thursday, and Saturday, and lied on the other days.
The Eveners spoke the truth on the even days of the week, on Monday, Wednesday, and Friday, and lied on the other days.
On the evening of his arrival, he had taken part in the arrest of some smugglers, and he had been beaten unconscious with a coconut. How long would he have been unconscious?

A nurse entered the room of the hospital and he heard a sweet voice asking how he felt. He quickly opened his eyes and saw that it was an indigenous inhabitant of the island.
“What day is it?” he asked.
“Tomorrow I will speak the truth,” she answered cryptically, in the same reassuring tone that some mothers use against their toddlers. Just before he lost conscious again, he realized that the nurse had actually answered his question.

What day of the week was it?

You can check your solutions here

Bongard problem (8)


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 8**
Bongard problem rule 11

You can check your solutions here

You can find more Bongard problems at Harry Foundalis site, and I intend to publish more problems in the future.

A new puzzle is published every 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.

Which day of the week?


2000px-Searchtool.svg

Fursters and Secunders – 1**/*****
Inspector Simon Mart had arrived on the island of Loginha. Half of the inhabitants, the Fursters, lie on Monday, Tuesday and Wednesday, and speak the truth on the remaining days. The other half of the population, the Secunders, lie on Thursdays, Fridays and Saturdays and speak the truth on the other days.

Inspector Simon Mart read through two interrogation reports and immediately noted a major omission: neither of them was dated, but he was assured that both had been written yesterday. One was an interrogation of a Furster, the other of a Secunder. Both contained the sentence “I lied yesterday”.

On what day did the inspector read the interrogation reports?

You can check your solutions here

Fursters and Secunders – 2*/*****
Inspector Simon Mart spoke to two people. One told him: “Today is Saturday”. The other told him: “Today is Sunday”.
If he does not know what day it is, can he deduce who is who?

You can check your solutions here

A new puzzle is published every Friday. You are welcome to discuss the difficulty level of the puzzles. Solutions are posted after one or more weeks.