10 logicians at the cafe

The two puzzles below are very easy. I am indebted to my long term friend Biep for passing this one on to me. There are some related puzzles, which you can find here and here.

Ten logicians walked into a cafe. Each knew whether they wanted tea or coffee, but no one knew each other’s preferences. When they sat at a table, the waiter asked loudly, “Will everyone be having coffee?” Then the waiter went around the table, writing down each person’s answer.
There were three possible answers: “I don’t know”, “Yes”, and “No”. All answers were truthful and spoken loudly so that all group members heard them.

I don’t know^*/*****
Suppose the first nine people said, “I don’t know”, and the tenth person said, “Yes”. How many of them wanted coffee?

6the and 7th^*/*****
Suppose the sixth and the seventh answers were not the same. How many people said, “I don’t know”, how many said, “No”, and how many said, “Yes”. Find the smallest number of people who for sure would have ordered coffee and the smallest number who for sure would have wanted tea?

You can check your solution here.

New puzzles are published at least once 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.

The successor of the sultan (4)

The sultan asked the vizier:
“The tests so far for finding my successor are way too easy. We’ve got to make them harder. There are still dozens of candidates left.”
“This one is definitely more difficult. First, they got to swim”
“So they had in the previous test,” the sultan grumbled.
“If they come up to breath, there heads will be shot off,” the vizier explained. The sultan nodded approval.
“There are four doors.”
“So had the previous test”
“But now there are two labels on every door. So they’ve got to think twice as fast!”

Test 4^***/*****

The first candidate look at the four doors.
“Again only one door hides a treasure,” the vizier explained. “There is a shark behind each of the other three.”
The candidate looked at the labels. He could see that there were two labels on each door, but he couldn’t read them.
“And how many labels are true? Or how many doors have true labels?”
“That is a very good question”, the sultan smiled. “As a matter of fact, knowing which door hides the treasure, it was impossible to decide upon the number of true labels. So how you should decide the number of true labels while you don’t know which door hides the treasure, is beyond me.”

Which door should the candidate open?

New puzzles are published at least once 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. You can check your solution here.

The successor of the sultan (3)

The ways in which the sultan of Buhrundipur choose his successor, were a bit, uh, unusual. He presented them with a series of tests. One by one he lead the into an empty basin with four doors.

Test 3^***/*****

“Only one door hides a treasure, the other doors hide a hungry shark. Oh, and only one label is true. Good luck!

Which box should the candidate open?

New puzzles are published at least once 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. You can check your solution here.

Knight or knave?

The well-known explorer Kickedoutofbed arrived a his first island in the Logico archipelago. He had been warned that there were two types of natives: Knights, who always speak the truth, and knaves, who always lie.

1) knight or knave?^**/*****
He met his first native right on the beach. Of course he was curious if the native was a knight or a knave, so he asked:
“Are you a knight or a knave?”
The answer came without hesitation:
“Yes, I am.”

Which of the two types is the native?

You can check your solutions here

New puzzles are published at least twice a month on Fridays.

Domino – lay out that set

Dutch puzzle designer Leon Balmaekers contacted me recently and told me he had written some booklets with puzzles for highly gifted children. The booklets are in Dutch, and contain a variety of puzzles. The highly gifted children in a classroom can make some of these puzzles when they have completed the normal exercises in a breeze.

One of the puzzle types uses a normal 0-6 domino set. Look at the figure in problem 1. In contrast to dominosa, the domino puzzle type most often used, the borders are clear, but the digits are missing.

Problem 1.^**/*****

The numbers along the sides are the sum of the pips in the respective rows and columns. It is up to you to figure out which domino should go where. Normal domino rules are followed: whenever two bones lay end to end, the numbers are equal.

For your convenience, here is a complete double 6 set:

You can check your solution here

Problem 2^**/*****

You can check your solution here

Problem 3^***/*****

You can check your solution here

A new puzzle is published at least once a month on the first Friday of the month. Additional puzzles may be published on other Fridays.

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.

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.

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?

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.



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?

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