Bongard and chatgpt


ChatGPT is a chat program based on a language model.

I had 2 sessions with it to test its ability to solve Bongard puzzles with language. I think its shows a severe limitation of the AI model used, though I have insufficient knowledge of AI to list

I will first list here the problems, please try to solve them yourself before turning to the solutions, where I will list the replies given by the AI bot.

Problem I*/*****
What is the difference between the sentences 1) to 6) and the sentences a) to f)?
1) What was Trumps salary as a president?
2) Why do many people like to solve puzzles?
3) How many puzzle magazines are sold yearly worldwide?
4) How many crossword puzzles has The Times published?
5) When will the next election in the Russian Federation be?
6) Who will likely be a candidate rivelling Abraham Lincoln as a president?
vs
a) Donald Trump recdeived the normalm salaray as a president
b) An oak tree can have over a thousand leaves
c) The Times published a crossword puzzle every day
d) Worldwide, puzzles are published in over 100 countries, and many magazines appear monthly.
e) It is widely regarded unlikely that the next election in the Russian Federation will be considered fair.
f) Forcing is a method used in set theory

Problem II*/*****
What is the difference between the tools 1) to 7) and the tools a) to g)?
1) Violin
2) drums
3) spanish guitar
4) irish flute
5) triangle
6) tambourine
7) organ
vs
a) Hammer
b) chisel
c) saw
d) drill
e) plane
f) pincers
g) screw driver

Problem III**/*****
what is the difference between the words in 1) to 7) and the words a) to g)?
1) float
2) make
3) produce
4) fly
5) write
6) think
7) speak
vs
a) fortress
b) idea
c) production
d) goods
e) article
f) booster
g) fire

Problem IV****/*****
What is the difference between the sentences 1) to 7) and the sentences a) – g)?
1) Jason was an argonaut
2) No duplication is OK
3) How many coins did I burn?
4) A fox obstructs my plan
5) Cats and dogs don’t munch grass
6) I saw an ox and an ass working as a pair is ridiculous
7) Who says I got no guts?

vs

a) I have no money left in my purse
b) Who says I have no courage?
c) volatile movements are normal on a stock exchange
d) Who stepped first into the elevator?
e) Gardens flower in spring
f) A sunny day raises the mood
g) “to jump” is a verb

Problem V**/*****
1) Bread can be brown
2) Bakers bake bread
3) Bookmakers bet money
4) Black is a beautiful colour
5) Bold soldiers fight on
6) Beraved of hope, the traveller sat down
7) Borrowing may cost you interest
vs
a) Shaving oneself may be a daily practice.
b) Silver is a precious metal
c) Sorry to hear that
d) Sending the message by telegraph is outdated
e) Skates can be used for matches
f) Samples are usually small
g) Singularities are abonormalities

Problem VI****/*****
1) Dogs bark loudly in our street
2) Mom bakes a delicious cake
3) Some countries ban books
4) The dad bears the financial responsibility
5) The kids become a little bit taller every day
6) Beggars beg for food
7) Christians believe the bible is true
8) The gambler bets
9) The police blocks the street
vs
a) This fish swims in the sea
b) The spy sabotaged the factory
c) The soldier salutes the flag
d) The soccer team scored another victory
e) I searched the internet in vain
f) John sharpens the pencil
g) John shaves himself

See here for the answers ChatGPT gave.

New puzzles are usually published on Friday mornings, on the first or third Friday of the month.

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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.

Bongard puzzle – back to math


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 conforms to a certain rule. Each box on the right contradicts this rule. Your task, of course, is to figure out the rule.

A Bongard problem consists of two groups of 6 images. Each and every of the six images on the left complies wit a certain rule. Each of the 6 images on the right does NOT comply with this rule. What is the rule?

THe title of this post already says this is a math puzzle, but you’ll first have to discover which branch of math, and than you will have to think about the one symbol which doesnt seem to fit into that branch.

Whats this?****/*****

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.

2023


Of course I wish all my readers a happy 2023!

1) 2023**/*****
Find two numbers a and b such that a^2 – b^2 = 2023.

2) 2023**/*****
Show that there is just one pair.

3) Difference*/*****
How much is 20232 – 20222?
This puzzle is an adaption of https://www.youtube.com/watch?v=NOIw0VZX1lc

Christmas was somehow more busy than I expected, so I apologize for not posting these puzzles earlier. However, here are some more 2023 brainteasers:
1) https://mathequalslove.net/2023-puzzle/*/*****
Sarah Carter made a puzzle by writing out the year with digital digits and cutting it up.

2) https://paulmotwani.com/2023/01/02/blog-post-145-happy-new-year-brainteasers-%F0%9F%98%8A%E2%99%A5%F0%9F%98%8A/**/*****
Paul A. Motwani brings a nice puzzle about a product and sum, which differ 2023.

New puzzles are published at least once a month on Fridays, usually the 1rst and / or third Friday of the month. 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.

Christmas puzzles 2022


Usually the puzzles in this blog are of the type “brainteasers”, uniquely constructed puzzles. There is another type of puzzles, which I call magazine puzzles. The best know examples are crosswords and sudoku. The latter have clear rules, a fixed format, but still every puzzle is different.

The puzzles I designed for Christmas 2022 are of the latter type. For each of the following five problems, the words have been taken from the Christmas stories in the classical King James translation. This alas results in some outdated words. Your task in each of the five problems is to fit the words into the yellow boxes.

It’s a tradition on this blog to publish a special blogpost for Christmas. People tend to have days off and spend more time with their family then during ordinary weeks. There is no advanced knowledge of the English language necessary. I wish you a lot of pleasure solving these puzzles.

Churches may use these puzzles for thei sunday classes, weekly newsletter, and similar publications, as long as you mention the source and don’t sue me. Copying materials is entirely your responsibility.

1) Matthew 1 **/*****
All words are used from left to right or top-down.

appeared
begat
brethren
brought
emmanuel
example
firstborn
forth
generation
minded
people

2) Matthew 2: 1-12 **/*****
All words are used from left to right or top-down.

bethlehem
days
demanded
diligently
eat
gathered
house
jerusalem
judaea
least
opened
priests
together
troubled

3) Matthew 2: 13-end */*****
All words are used from left to right or top-down.

appeareth
called
children
comforted
destroy
egypt
enquired
herod
jeremy
lamentation
might
prophet
prophets
rachel
under

4) Luke 1 : 1-22***/*****
Words can not only be filled in top-down and from left to right, but also starting at bottom and from right to left.

appeareth
called
children
comforted
destroy
egypt
herod
jeremy
lamentation
might
prophet
prophets
rachel
under

5) Luke 1 : 22-end***/*****
Like the previous one, words can be in any direction: top-down, down to top, left to right, or right to left.

accomplished
cousin
darkness
dayspring
delivered
deserts
elisabeth
espoused
highly
hungry
joseph
leaped
ministration
neighbours
overshadow
promised
prophets
reproach
salutation
saluted

I apologize beforehand if there are any undetected errors in the puzzles. Please check them before copying them in any other medium.

You can find the solutions here.

Bongard and history


Today we expand Bongard puzzles into the realm of history.

The Bongard puzzle below shows three boxes. Each box lists 6 or 7 historical persons. According to What secret rule(s) have they been grouped? What is the logic?

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.

Labeled numbers (2)


Four of the five numbers below have a label consisting of three letters. Every letter stands for a property of the associated number.

Difficulty: ****/*****
The question is: what label belongs to the number in the middle?

A new puzzle is published at least once a month on Friday. You can check your solution here.

Did you like this puzzle? The good news is I wrote a booklett with dozens of these puzzles, you van find it here.

Three


Use 0, 0 and 0 to make 6
Use 1, 1 and 1 to make 6
Use 2, 2 and 2 to make 6
Use 3, 3 and 3 to make 6
Use 4, 4 and 4 to make 6
Use 5, 5 and 5 to make 6
Use 6, 6 and 6 to make 6
Use 7, 7 and 7 to make 6
Use 8, 8 and 8 to make 6
Use 9, 9 and 9 to make 6
Use 10, 10 and 10 to make 6

You can use the numbers and any mathematical function such as sqrt() (√). You are not allowed to introduce other numbers.

An example of a solution could look like: 3×3-3 = 6

A new puzzle is published at least once a month on Friday. You can check your solution here.

Did you like this puzzle? The good news is I wrote a booklett with dozens of these puzzles, you van find it here.

Labeled numbers


Four of the five numbers below have a label consisting of three letters. Every letter stands for a property of the associated number.

Difficulty: ****/*****
The question is: what label belongs to the number in the middle?

A new puzzle is published at least once a month on Friday. You can check your solution here.

Did you like this puzzle? The good news is I wrote a booklett with dozens of these puzzles, you van find it here.

Cryptarithms WATER and OCEAN


Everybody knows that for an ocean you need lots of water. But how much?

In the following addition,
WATER
WATER
WATER
WATER
—–+
OCEAN

Replace every letter with a digit to get a correct addition.
The same letter always represents the same digit and no digit is represented by 2 or more letters.

Funny enough, we can also reverse this:
OCEAN
OCEAN
OCEAN
OCEAN
—–+
WATER

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 solutions here.