Tag Archives: Brainteaser

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.

cryptarithm: worship


Alphametic**
This weeks puzzle has a christian theme. In this alphametic, replace every letter with a digit. The same letter always represents the same digit and identical digits have always been replaced by the same letter:

Cryptarithm 2016-06-11 nr 1 exericse

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 three stars.

How many?


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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.

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?


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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.

Squares


It is trivial to divide a square into 4 squares:
Divide a square exercise illustration

Divide a square into:
a) 6 squares
b) 7 squares
c) 8 squares (2 ways)
d) 9 squares (2 ways)
e) 10 squares (2 ways)
f) 11 squares
The squares should not overlap.

A new puzzle is posted every friday. You are welcome to comment on the puzzles. Solutions are added at the bottom of a puzzle after one or more weeks.

You can check your solutions here

Calculating the roman pantheon


Header image problemThe Roman pantheon consisted of a large number of deities.

The Roman chronicler Problematus recorded that a limited number of their gods would be sufficient to have as deities. He noted this because you could have a sum of four numbers, and replace digits with letters (always replace the same digit with the same letter), and get:
Alphametic roman pantheon

What numbers do the letters stand for?

You can check your solutions here

The hiker, the bicycle and the moped


Hiker, cyclist and moped


Alexandra, Bernadette and Cindy all want to go from A to B. The distance is 60 km. (If you prefer miles, simply read miles instead of kilometers in this puzzle.)

They have a bicycle and a moped. Both are without backseat, so only one person can use them at any time.
A hiker walks 5 km/hour.
A Cyclist goes 10 km/hour.
The moped rider makes 20 km/hour.

A hiker would take 60/5=12 hours.
A cyclist would take 60/10=6 hours
The moped rider would take 60/20= 3 hours.
Together that is 12+6+3=21 hours, or 7 hours average.

Is there a way, by alternating transport means, that the three people all can make it in 7 hours?

If you are stuck, one possible solutions is given here. Be aware that more solutions are possible.

This puzzle is based on a similar problem in Pythagoras, issue 1 1967/1968. The distance and the speeds have been changed.

It is easy to see simplify this problem to 2 persons, A and B. The solutions become pretty trivial. But how about expanding the puzzle to 4 people, or 5, or even to n people?

A new puzzle is published every friday. You are welcome to comment on the puzzles. Solutions are usually added after one or more weeks.