Category Archives: Deduction

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.

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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

The 4 cards (Cont’d)


The brainteaser of the 4 cards is a nice teaser, which made me wonder if it could be generalized. Indeed I found a couple of ways to vary upon this theme.

1) The 3 values
There are six cards in front of you. Each of them has a letter on one side and a number on the other side. Three of them have letters face up: A, B and C. The other three have numbers face up: 1, 2 and 3.
How many cards (and which) do you want to check if you want to know every card with ‘C’ on the front face has a ‘2’ on the reverse?
6 cards

You can check your solutions here

2) The three triangular blocks
Another way to vary on this subject is to have more than one backside. Consider the wooden blocks depicted in this figure. They have three sides (plus a top and a bottom). One side has a letter, one side a color and one side a number. Only one side is facing you. You can only rotate them clockwise. You are not allowed to get up and walk around them.
As you can see, each block now has two ‘backsides’, a leftback and a rightback. The letter is either A or B, the number either 1 or 2, and the colour either orange or purple.
3 blocks


As you can see there is an ‘A’, a ‘2’ and an ‘Orange’ facing you.

How many rotations do you have to make to ascertain if the rightback of all B is purple?

You can check your solutions here

The 4 cards


Before you are four cards on the table. The front side has an ‘A’ or a ‘B’ on it. The back has a ‘1’ or a ‘2’ on it. As you can see, two cards show their front side, and the other two cards show their back side.
A friend of mine thinks that on the back of every card with a ‘B’ there is a ‘2’.
Which card(s) do you turn to test his hypothesis?

AB12

This is not an original problem, and the source is unknown to me. I guess it is from somewhere in the twentieth century. I was recently reminded of it when thumbing through James Fixx “More games for the superintelligent”, a mensa publication. I hope to get back to this puzzle in a later post.

You can check your solutions here

Tectonics


The free Dutch daily newspaper Metro recently – I think it was in september – published a new type of puzzle calles tectonics.
The puzzle area usually is a rectangle, for example 4×5, which is subdivided into areas of size 1 to 5. An area of size 1 contains just the number 1, an area of size 2 contains the numbers 1 and 2, and so on, until an area of size 5 which contains the numbers 1, 2, 3, 4 and 5 exactly once.
A second rule is that the same number may never be adjacent: not horizontally, not vertically, and not diagonally.
Note that there is no rule that a number may appear just once in a row or column.

A complete filled tectonic may look like:
tectonic example solution

The puzzles in Metro are designed by Denksport, the largest puzzle publisher in the Netherlands. In the magazine shop I discovered a magazine with these puzzles.
Tectonic puzzle booklet can be ordered here. I think the order page is only in Dutch, and I’m not sure if you can mail order from abroad.

Nr 1)*
Tectonic 2015-10-15 5x10 exercise nr 1

Nr 2)*
tectonic 2015-10-14 nr 3 exercise

Nr 3)**
Tectonic 4x5 2015-10-15 nr 2 exercise

You can check your solutions here, here, and here.

The publisher claims that these puzzles are a new international rage. That may well be true, but a quick search on “tectonic puzzles” turned up just puzzles on plate tectonics.

Inspector Simon Mart and the stolen matchsticks


2000px-Searchtool.svgInspector Simon Mart looked at the old sign on the door of his office with his name: Inspector Mart, S. That his parents had bestowed just one initial on him, had been one of his life long irritations. He probably should have told his parents before his birth that he wanted many birth names. But perhaps he could persuade the guys who provided the signs on the doors that his initial should precede his family name, and not come after it. Well, he had his own room and that was a benefit that should last until the next reorganization.

His manager had dumped a file on his desk. He read the attached note: ‘to be solved last month’. It was the 29th of the month, and he decided that this urgency would allow him to start with a mug of coffee and a social chat with his fellow inspectors at he coffee machine. At the coffee machine he met a new and pretty police officer and he chatted for a quarter of an hour with her. After that chat he decided to pick up this file. It contained a number of reports as well as a copy of interrogations. He summoned that a couple of matchsticks encrusted with amethysts had been stolen from the London Matchbox Museum. There were three suspects, Jim, Jack and John, all well known criminals. It was known that none of them could speak two consecutive true statements. He looked at the interrogation reports:

Jim: Jack did it. John is innocent.
Jack: John did it. Jim is innocent.
John: Jim is innocent. Jack is innocent.

You can check your solutions here

Shikaku


Shikaku puzzles are puzzles which can be found in some magazines. They were invented by Nikoli, a Japanese puzzle firm. Allthough they can be drawn in black and white, the colored versions seem to be more popular. There are several websites offering them – see below They are also known as Shikaku ni Kire, rectangles, Divide by Squares and Divide by Box.

The basic is a square or rectangle which has been subdivided into rectangles. The border lines are not shown in the exercise – this is what the solver has to find out. The sizes of the rectangles are given as clues.

Example:
shikaku 5x5 exercise

The solution:
shikaku 5x5 nr 1 solution

As you can see in the examples above:
(1) Only rectangles are used;
(2) Every rectangle has exactly 1 square indicating its size;

Here are some puzzles with them:
1) Problem 6×6

shikaku 6x6 nr 1 exercise

2) problem 7×7

shikaku 7x7 nr 1 exercise

3) problem 12×12

shikaku 2015-03-05 12x12 exercise

There are several apps for your android smartphone or ipad around. Sites which offer shikaku puzzles are:

  1. http://www.nikoli.com/en/puzzles/shikaku/
  2. http://www.mathinenglish.com/Shikaku.php

You can check your solutions here, here and here

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?

If you wish you can check your solution.

Three students


envelopAlex is an art-student who sends an email to Bert. Charles is not an art-student. Bert sends an email to Charles.

Now the simple question is: Does an art student send an email to someone who is not an art student?

Yes or No? Or can’t decide because of lack of information?.

This puzzle comes from a presentation by Paul Fenwick, which you can find here

If you solved it, we have the solution so you can check yours.

Perfect logicians


Pirate smiley1) The five pirates**
Five pirates have 100 gold pieces. They are all perfect logicians, greedy , and blood thirsty.

They have a strict order of seniority, and the most senior pirate makes a proposal how to divide the 100 gold pieces among them. The pirates vote on the proposal. If the proposal is accepted (more votes for than against, or the number of votes are equally divided), the 100 gold pieces are divides as per proposal.
The gold pieces can not be divided into fractions, and all pirates are know that the others are logical too. Moreover, they don’t trust each other, so any deals among the pirates are not possible.

If the proposal is rejected (at least as many votes against as in favour of the proposal), the pirate who made the proposal is killed and the pirate who is next in order of seniority makes a proposal. That can continue till there is just one pirate left.

When casting his vote, the priorities of each pirate are:
I) Stay alive himself
II) Get as much gold as possible
III) Kill off other pirates
All 5 pirates are perfect logicians, and immediately sees the result of any proposal and will, with the a fore mentioned priorities in mind, cast his vote.

Which proposal should the most senior pirate make?

2) Five pirates again**
This puzzle is the same as above, with two changes:
a) If the votes on a proposal are equally divided, the proposal is rejected.

3) How many pirates?**
How many pirates can take part in the division of 100 gold pieces, with the rules from puzzle 1, with the first one still surviving? And how does the pattern develop with an ever increasing number of pirates?

There is of course no intrinsic reason why the persons in this puzzle should be pirates. They could easily well be immigrants from Pluto on Mars, or be hula-hoop girls on a remote pacific island. I have retained the pirates as figures because people are most likely to search for this word when trying to study this puzzle.

If you solved it, we have the solution to 1

If you solved it, we have the solution to 2

If you solved it, we have the solution to 3