Tag Archives: Brainteasers

Bongard problem 40


Which rule satisfies the 6 figures on the left but is obeyed by none of the 6 figures on the right?
1)Bongard problem 40***/*****


In 1967 the Russian scientist M.M. Bongard published a book containing 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.

You can check your solution here

You can find more Bongard problems here on this site and at Harry Foundalis’ site.

Pradeesh Mutalik can be credited for taking Bongard problems from the realm of geometry to the realm of numbers and language.

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.

Bongard problem 37


Which rule satisfies the 6 figures on the left but is obeyed by none of the 6 figures on the right?
1)Bongard problem 37**/*****



All letters used have font size 48.

In 1967 the Russian scientist M.M. Bongard published a book containing 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.

You can check your solution here

You can find more Bongard problems here on this site and at Harry Foundalis’ site.

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.

2019


1) Make 2019 (1)**/*****
Take the series 1,2,3,4,5, etc. Insert + and – signs in between the numbers to make 2019. Do not use brackets. What is the shortest series?

2) Make 2019 (2)***/*****
Take the digits, 0-9. Keep them in exactly this ascending sequence and combine them wit +, -, *, /, ^, brackets and/or ! to make 2019.

3) Make 2019 (3)***/*****
Take the digits, 0-9. Order them in descending sequence (9, 8, 7, down till 0) and combine them with +, -, *, /, ^, brackets and/or ! to make 2019.

4) The digits 2, 0, 1, and 9***/*****
The year 2019 is made up of the digits 2,0,1 and 9. Combine them with all mathematical and arithmetic operators to make every number 0-20. For example: 0*1*2*9=0.

5) The digits 2, 0, 1, and 9***/*****
The 9 is the largest digit in “2019”. It is the square of the sum of the three other digits (9 = (2+0+1)^2). What is the next year when the largeest digit is euqal to the square of the other three digits?

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.

Billy’s Big Christmas Party


Billy was delighted to have gained entry to the Big Christmas Party in the neighbouring village. There were stalls and booths littered throughout the hall.

1) The apple pie stall**/*****
The first stall he walked to showed delicious steaming hot pieces of apple pie on display. Several other kids had gathered in front of it.
A sign read:
4 and 7 give 33
3 and 2 give 5
8 and 5 give 39
A middle aged lady behind the stall held up two numbers: 6 and 3.
“This woman must be the wife of the math teacher,” he whispered to his neighbour.
The lady must have overheard him, because she laughed:
“Young man, I am the math teacher.”
But she was quickly satisfied when Billy quickly figured out the correct answer, collected his piece of apple pie and walked to the second stall.

You can check your solution here

2) The hot chestnuts stall****/*****
The second stall displayed dishes of chestnuts filled with had chestnuts. A man was roasting the chestnuts on a small coal fire and serving them with several sauces.
A sign displayed some calculations:
11 + 11 = 8
12 + 59 = 18
18 + 47 = 16
23 + 39 = 16
He held up two numbers for the children in front of his table: 22 and 45.
Slightly softer than the previous time, Billy whispered to the girl besides him:
“Do they have two math teachers here?”
The girl looked at him saying:
“Did you ask if we have two math teachers here?”
The man heard it and laughed: “No, I’m the Arts teacher.”
Billy quickly grasped the problem and found the sum of 22 and 45.

You can check your solution here

3) The mince pies****/*****
The third stall displayed a lovely looking plate with mince pies.
A piece of cardboard listed:
5 and 6 give 6
3 nd 7 give 7
7 and 8 give 8
She held up two cards showing 4 and 12. “What number do they give?” she asked. “I’ll tell you in advance the answer is not 12.”
To prevent him from asking, the girl besides him told him:
“No, she doesnt teach math. She teaches English.”

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.

Bongard problem rule 21


Which rule satisfies the 6 figures on the left but is obeyed by none of the 6 figures on the right?
1)Bongard problem 21**/*****


In 1967 the Russian scientist M.M. Bongard published a book containing 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.

You can check your solution here

You can find more Bongard problems here on this site and at Harry Foundalis’ site.

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.

Bongard problem 35


Which rule satisfies the 6 figures on the left but not the 6 figures on the right?

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.

You can check your solution here

You can find more Bongard problems here and at Harry Foundalis site, and in the category ‘Bongard problems’ in the right margin of this page.

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.

numbers 2, 3 and 5


A couple of years ago I posted the problem of four fours.

Recently I stumbled upon Gene Wirchenko’s Blog, and he had s similar problem.

Here is a variation of his problem. Combine 2, 3 and 5 to make all the numbers 0-22. Use each of the three digit exactly once, but you are free to use addition, multiplication, division, subtraction, brackets, exponentiation and factorial as often as you like.
For those of you who are not familiar with factorials a short reminder:
0! = 1
1! = 1
2! = 2*1
3! = 3*2*1
4! = 4*3*2*1
etc.

You can check your solution here

New puzzles are published at least twice a month on Fridays. Solutions are added after several weeks.

Matchsticks – a diamond


Have a look at at this diamond – it is made up of 10 triangles.

Your challenges are:
1) 8 triangles**/*****
Move 4 matchsticks and have 8 triangles

2) 7 triangles**/*****
Move 4 matchsticks and have 7 triangles

3) 6 triangles**/*****
Move 4 matchsticks and have 6 triangles

4) 5 triangles**/*****
Move 4 matchsticks and have 5 triangles

You can check your solution here

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

Truth-speakers, Switchers and Liars at the table in the restaurant


In the restaurant***/*****
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.

In a restaurant, a group of natives are sitting at a circular table.
They take turns to say: the person to my left is a Switcher.
After that, they take turns, starting with the same person, to say: the person to my left is a Liar

What can you say about their type? How many are Truth-speakers? How many are Switchers? How many of them are Liars?

You can check your solution here

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