Category Archives: Logic

Bongard problem 10


Which rule satisfies the 6 figures on the left but is obeyed by none of the 6 figures on the right?
1)Bongard problem 10***/*****


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.

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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 36


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.

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.

River crossing


In the past I published several posts on river crossing puzzles. I think together they are the most extensive resource on river crossing puzzles on the web.

I used the week between Christmas and New Year to look for apps. To my surprise, there was just one, and it held just a few puzzles. Well, it did in spire me to:

1) The Autists and the Lazy.
Six people want to cross a river. They have a boat which can hold only 2 people at a time.
* Two of the six people are autists. They don’t want to be in the boat with any one else, though they don’t mind being on the same shore.
* Two of the people are outright lazy, and don’t want to row.
* The remaining two people are normal.
How many crossings does the boat have to make?

You can find the old posts here:
* Man, wife and kids – river crossing 1
* The farmer, the wolf, the goat and the cabbage – 2
* Three couples – river crossing – 3
* Bigamists – river crossing – 4

New brainteasers are published twice a month on Fridays.

You can check your solution here