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.

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.

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.

Bongard plants puzzles

This month we move with our Bongard problems to biology, more specific to the area of plants.

If you already know how Bonmgard problems work, you can skip the explanation and go directly to the problems below.

If you don’t know what a Bongardproblem is: A Bongard problem consists of two groups of 6 (or more) items. Six on the left, and six on the right. The question is: what is the difference between the items on the left and the items on the right?
To be more precise: there is something the six items on the left have in common, while none of the items on the right have this property. What is this secret rule that the items on the left have?

1) Plants(1)^*/*****

2) Plants(2)^**/*****

3) Plants(3)^***/*****

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.

Bongard puzzle tanach / bible (2)

This Bongard puzzle is about donkeys. What is the difference of the texts on the left and those on the right?

If you don’t have a bible, you can check them out at at biblestudies.com.

1) Donkey / ass^**/*****

Any one of the following translations are OK:
* King James Version
* New International Version
* New Revised Standard Version
I could have written them out, but I don’t want to run into copyright problems. And in tis format you can easily copy them into the weekly newsletter of your synagogue, church or sunday school.

What makes a Bongard puzzle a Bongard puzzle?
If you are used to Bongard puzzles, you may miss the 2 x 6 familiar boxes, and wonder what exactly makes a Bongard puzzle a Bongard puzzle.
In its original format, a Bongard puzzles consisst of 2 groups of 6 drawings. There is a secret rule which differentiates the two groups. Each of the drawings in one group obeys thes secret rule, while each of the items in the other group contradicts the=is rule.

The essence to me is not in the boxes. In the puzzle above I have grouped 12 texts in two rectangles with each 6 textxs. That still leaves 12 items to compare.
Are the numbers 6 and 12 essential? My answer is: No, thje system would function as well with two groups of 7 items, of with a group of 5 and a group of 8 items.
My definition of a Bongard puzzle would be:
a) There are 2 groups of items
b) Each of the items in one of the groups is an example of a secret rule.
c) Each of the items in the other group contradicts this rule.

What happens if we increase the number of groups from 2 to 3?
For example:

I would like to coin the term: ‘Bongard-like puzzle’ for these puzzles. There are clearly some Bongard puzzle features. There are secret rules for each of the three groups of numbers. The groups are mutually exclusive, just as the two groups in a Bongard pouzzle are mutually exclusive. So each of the members of the other group can be considered counter examples to the rule of the first group.

But it does depend on definition.

Pentecost

Here’s a Bongard problem for you, though I didnt mold it into the 2×6 traditional boxes:

Have a look at the following story of pentecost. I have taken it from the new King James Version, Acts 2:14-36.

The question is: in what way are the verses 17, 18, and 33 different from the other verses?

14 But Peter, standing up with the eleven, raised his voice and said to them, “Men of Judea and all who dwell in Jerusalem, let this be known to you, and heed my words.
15 For these are not drunk, as you suppose, since it is only the third hour of the day.
16 But this is what was spoken by the prophet Joel:
17 ‘And it shall come to pass in the last days, says God, That I will pour out of My Spirit on all flesh; Your sons and your daughters shall prophesy, Your young men shall see visions, Your old men shall dream dreams.
18 And on My menservants and on My maidservants I will pour out My Spirit in those days; And they shall prophesy.
19 I will show wonders in heaven above And signs in the earth beneath: Blood and fire and vapor of smoke.
20 The sun shall be turned into darkness, And the moon into blood, Before the coming of the great and awesome day of the Lord.
21 And it shall come to pass That whoever calls on the name of the Lord Shall be saved.’
22 “Men of Israel, hear these words: Jesus of Nazareth, a Man attested by God to you by miracles, wonders, and signs which God did through Him in your midst, as you yourselves also know–
23 Him, being delivered by the determined purpose and foreknowledge of God, you have taken by lawless hands, have crucified, and put to death;
24 whom God raised up, having loosed the pains of death, because it was not possible that He should be held by it.
25 For David says concerning Him: ‘I foresaw the Lord always before my face, For He is at my right hand, that I may not be shaken.
26 Therefore my heart rejoiced, and my tongue was glad; Moreover my flesh also will rest in hope.
27 For You will not leave my soul in Hades, Nor will You allow Your Holy One to see corruption.
28 You have made known to me the ways of life; You will make me full of joy in Your presence.’
29 “Men and brethren, let me speak freely to you of the patriarch David, that he is both dead and buried, and his tomb is with us to this day.
30 Therefore, being a prophet, and knowing that God had sworn with an oath to him that of the fruit of his body, according to the flesh, He would raise up the Christ to sit on his throne,
31 he, foreseeing this, spoke concerning the resurrection of the Christ, that His soul was not left in Hades, nor did His flesh see corruption.
32 This Jesus God has raised up, of which we are all witnesses.
33 Therefore being exalted to the right hand of God, and having received from the Father the promise of the Holy Spirit, He poured out this which you now see and hear.
34 For David did not ascend into the heavens, but he says himself: ‘The Lord said to my Lord, “Sit at My right hand,
35 Till I make Your enemies Your footstool.” ‘
36 “Therefore let all the house of Israel know assuredly that God has made this Jesus, whom you crucified, both Lord and Christ.”

You can check your solution here.

Bongard – Letters

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?

Letters^***/*****

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.

I am indebted to Monday Math for the idea for this rule. See video https://www.youtube.com/watch?v=w5oprHOE0NU.

Bongard – Letters

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?

Letters^***/*****

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.

My apologies for the absence of a monthly Bongard puzzles in the first three months of 2022. I hope to pick up this again on a monthly basis.

Bongard: lines and circles

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?

Lines and circles^**/*****

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.

Counting dots and infinity

The following Bongard problem was devised to be added to my book “Bongard puzzles for Kids”.

Which differences do you see between the 6 images on the left and the 6 images on the right? Yes, there is more than one difference. How many of them can you spot?

And more interesting perhaps: how many differences do you think there are? Or, more in terms of Bongard problems: How many rules are there which describe the 6 figures on the left, while non of the 6 images on the right comply with this rule?
Now think a while before you scroll down.

Oh, one last bit. A couples of differences are listed here.
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Actually, the number of rules is infinite. Surprise?

Let me try to show this. There are at least three ways to show that. All three ways need some math, but we’ll start with the easiest way. In subsequent posts I hope to move towards a more rigorous proof.

But we’ll take a bit of a detour.

Let’s start with a “list of numbers” puzzle, where you are asked to expand a short list of numbers with the next number. You often encounter them in many IQ tests.
Let’s have a look at this one:
1, 3, 9, 27, ….
What is the rule? What is the next number?
You probably answered ‘81’, didn’t you? You noticed that the rule seemed to be that every number was 3 times the previous number.
But is that the only rule that explains this sequence of 4 numbers? No, there are at least 2 other rules. One is, that every number is odd. So the next number might be 81, or 29, or even a lower number such as 7. A second rule that describes this sequence is that every number must be higher than the previous one. 81 would still be good, but so would be 28 or 29. And a third possible rule: the numbers 1, 3, 9, 27 are repeated over and over again.

These examples show that such a simple sequence of numbers has multiple solutions. But multiple solutions is not the same as infinitely many solutions.

How do we find infinitely many rules that explain 1, 3, 9, 27, …? Well, one possibility a variation of the third rule suggested above. Suppose the rule is that the numbers 1, 3, 9, 27, 31 are repeated over and over again. Or 1, 3, 9, 27, 28. Any number can be used as the fifth number. Arbitrarily? Absolutely! Ugly? Yes! Artificial? Yes! But nevertheless the four number sequence comply to these rules. You may object that these rules are ugly. You may object that these rules have no way to be predicted. And you are absolutely right. Only if we had a sequence 1, 3, 9, 27, 28, 1, 3 we would have a reasonable base tot suspect that there is a repeating group in this rule. With just four numbers, in ascending order, we have no base to suspect there is a repeating group. But neither can we exclude it. But for the four numbers we started with: they do comply with the rule.

So far for expanding a list of numbers. But there are still two missing steps. The first missing step is: What is the relation between the Bongard puzzle and a list of numbers? The second step is: What about the six diagrams on the right? Don’t the cross out those infinitely many rules?

As for the question how we get from Bongard problems to numbers: Let’s say each square is 100 x 100 pixels. A pixel can have 16 million colors. So the first pixel can have a 16 million values. And with 100 x 100 pixels, we have 10.000 pixels.
But we need something more.
We are going to map all 10000 pixels to a unique number.
Number the pixels p1 to p10000.
Now take
value of (p1) * 16M^0 +
value of (p2) * 16M^1 +
value of (p3) * 16M^2 +
…
value of (p10000) * 16M^9999
Yeah, they are pretty big numbers. Your life here on earth would be too short to count them, but there is nothing here our math can’t handle.

The second step which we so far did not touch, is the question how many rules are cancelled out by the 6 examples on the right. That is something for another post.