# 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?

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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?

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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?

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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?

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# How many?

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.

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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)

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

# Which day of the week?

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?

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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.

# Inspector Simon Mart and the stolen toupet

Inspector Simon Mart looked out of the window of his familiar office room. What he saw was very familiar: nothing. Or, more precisely: the well known grey of London smog. It looked like a particular dense smog, as he could not even see the tree at the other side of the street, nor the pedestrians or traffic in the street below.

He would much, much rather have been at the sun drowned beaches of a tropical archipellego, but he was here back in London.
And he’d better get to work. He looked at the interrogation reports of the three criminals. The toupet of major Big Boaster had been stolen. The three criminals were all so rotten that none of the three could utter three sentences without speaking the truth more than once. Luckily, it had already been established that one of them was the thief.

Their interrogation reports:
Picking Pete: Rotten Ray is innocent. Thoughtless Theo is the thief. I am innocent.
Rotten Ray: To his dismay inspector Mart found that some thoughtless secretary had spilled coffee over this interrogation report, and it was completely unreadable.
Thoughtless Theo: Picking Pete is innocent. I am innocent. Rotten Ray is the thief.

Inspector Simon Mart got himself some tea from the coffee maachine and found that it tasted just like one can expect from a coffee machine: the tea tasted as coffee.
Still, he managed to conclude who the thief was. Can you?

You can check your solutions here

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.

# Inspector Simon Mart and the stolen matchstick

‘I was on the island of Lotl Ire Esain in the Archipellago,’ Inspector Simon Mart wrote in his text editor, ‘where I encountered a strange case. The island is remarkable ny its population, which consists of two distinct groups: Liars, who will always Lie but are honest in the sense that they will never steal, and Thieves, who will often steal but who are absolutely honest in that they will always tell you the truth.’

He continued to write:
In one case brought to my attention, a person had been robbed of a box of burnt matchsticks. Now that may sound ridiculous, but the island is devoid of trees and all wood must be imported so it is considered a criminal offense.

Two suspects were brought in, and it had already been established that one of them had to be the criminal. The policeofficer who brought them in introduced them as Peter and Paul.
‘What the hack,’ I thought. ‘Would it have been the same two persons or is every Jack and Joe called Peter and Paul here?’ Anyway, hoping that the thief would simply asnwer truthfully, I asked Peter: ‘Dit you steal the matchstick?’
But Peter simply answered: Paul is a Liar.
Asking Paul the same question to Paul, Paul replied: ‘Peter is a thief’.

Who stole the matchstick?

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# Inspector Smart on the Isle of Thieves and Liars

After his adventure on the island of Koaloao, Inspector Simon Mart traveled on to the second island in the Logico archipelago, Lotl Ire Esa.

The population of this island, he knew, was very peculiar; it consisted of two distinct groups, each with his own rigid disposition, and the inspector suspected it was a genetic mutation.
One group on this island was called Thieves: they had an uncontrollable tendency to steal, but they would always tell the truth. The other group was called Liars, they never stole anything but would always lie.

1) The scepter of dignity
After checking into his hotel, he had gone straight to the police headquarters in the capital. In the case before him, there were two suspects, Peter and Paul. The crime under investigation was the theft of the Scepter of Dignity, a rod made of used matchsticks, and dating back to 1997.

Peter: Paul is a Thief. But he did not steal the scepter.
Paul: Peter is a Thief. And Peter stole the scepter.
It was already certain that one of the two had stolen the scepter. Who is guilty?

If you wish you can check your solution.

# Inspector Simon Mart and the camper at Trafalgar square

Inspector Simon Mart looked at the blank screen of the word processor in front of him. He really wanted to write down something about the interesting cases he had explored at the isle of KoaLoao. He was glad, of course, to be back in London, back in the familiar office, back between the familiar colleagues at Wales Yard, back in his own familiar office room with the familiar mug of the familiar undrinkable drab of coffee.
Just as a blink of inspiration on how to start popped up, a superintendant dropped in, wiping out any trace of inspiration about how to start.
‘Three suspects of the theft of the copper kettle of a camper on Trafalgar Square, Simon. Can you question them? Boring cases, of course, for you, after your holiday in Archipelagio.’
‘The only one who needs to be questioned is the camper,’ Simon replied dryly. ‘Why would any one in his right mind want to put up his tent there? Did he obstruct the traffic? And why would he have a copper kettle where every camper uses plastic stuff?’
‘I admit we made a Strategic Mistake in letting that guy go,’ the superintendant replied with a devilish smile, ‘He didnt seem to have obstructed the traffic – he put up his tent in the fountain. But the three suspects we rounded up are all we have. Oh, and we are sure one of them did it.’ Having said that, he showed in Mighty Mike, Ron Rubbish and Sluggy Sarah.
Inspector Simon asked them one simple question: ‘Who did it?’
Mighty Mike replied: Ron Rubbish did it.
Ron Rubbish answered: Sluggy Sarah took it.
Sluggy Sarah said: I’m innocent.
Now, assuming only the thief lied, who should the inspector keep in custody for further interrogation?

You can check your solution here

# The Babuschka and the pearls

Before going home, Inspector Simon Mart visited a pearl shop on the island of KoaLoao, where every native was either a TruthTeller or a LieSpeaker, he decided he really had to take home a souvenir.

He looked around in one of the local pearl shops. It was not very large, but his eye fell on a nicely crafted Babuschka – one of those russian dolls where, when you open it, it contains another similar doll, which, when you open it, ok, you get it.
This babuschka contained 3 smaller dolls, and had six small pearls inlaid for the eyes of the dolls. He picked it up and weanted to buy it, but his eye fell on a pillow with 4 beautiful large pearls, some entire white, some entirely black. He remebered that all pearls on this island were either black or white.
“How many of these large pearls do you have?” Simon asked, interested.
“Not very many” the shopowner asnwered. “My neighbour next door has more, and he has 29 pearls of this size.”
“That doesnt tell me how many you have” the inspector remarked.
“Well, if I would put all my large pearls in a bag, both black and white, and you would take out two at random, the chances would be exactly 1 in 5 that you would have two black ones.”
“Don’t believe a word he says!” the servant in the shop warned him. “My boss is a notorious LieSpeaker! Our neighbour has 30 pearls of this size, and the chances are exactly 1 in 4 that you would take out 2 white pearls!”

“That makes things clear!” answered inspector Mart. “Thank you!”

How many pearls does the shop owner have? And who is speaking the truth?

Please try to solve the puzzles on your own. You are welcome to remark on the puzzles, and I love it when you comment variations, state wether they are too easy or too difficult, or simply your solution times. Please do not state the soultions – it spoils the fun for others. I usually make the solution available after one or two weeks through a link, which allows readers to check the solution without the temptation to scroll down a few lines before having a go at it themselves.

When you have solved this puzzle, you can check your solution here