Solve without algebra

[Genady]

How tall is the table?

BTW, I could not make ChatGPT answer this question correctly, with or without algebra.

[mistermack]

Spoiler

150

 

[Genady]

Just now, mistermack said:

  Hide contents

150

 

Correct. +1.

Couple words, hidden, about your "trick"?

[mistermack]

13 minutes ago, Genady said:

Couple words, hidden, about your "trick"?

Spoiler

An old trick I use all the time, of not reading the question properly. 🤔

 

[Genady]

5 minutes ago, mistermack said:

  Hide contents

An old trick I use all the time, of not reading the question properly. 🤔

 

Spoiler

OK.

Don't let it stop you from trying other tricks 😉

 

[mistermack]

29 minutes ago, Genady said:

Don't let it stop you from trying other tricks 😉

Spoiler

To be honest, I'd forgotten what algebra meant. Doing it from a mental picture, I would stack the left table on top of the right one. 

You then have the two measured distances sitting on top of each other, totalling 300cm. Drop them down by one cat, and the two tables 

are equal to the the two measured distances, of 300 so, one table is 150.

I don't know if I'm unconsciously using mental agebra in that process though.

 

Edited June 6, 2023 by mistermack

[Genady]

3 minutes ago, mistermack said:

  Hide contents

To be honest, I'd forgotten what algebra meant. Doing it from a mental picture, I would stack the left table on top of the right one. 

You then have the two measured distances sitting on top of each other, totalling 300cm. Drop them down by one cat, and the two tables 

are equal to the the two measured distances, of 300 so, one table is 150.

I don't know if I'm unconsciously using mental agebra in that process though.

 

That's what I meant "without algebra", and that's the same mental picture I've used. +1

[TheVat]

Spoiler

My trick was to average the two given heights.  150.

Any two animals, if you make them both the average of their two statures, then their top to top distance will be table height.

 

[Genady]

4 minutes ago, TheVat said:

  Reveal hidden contents

My trick was to average the two given heights.  150.

Any two animals, if you make them both the average of their two statures, then their top to top distance will be table height.

 

Cool. This works, too. +1

And gives me idea for another trick:

Spoiler

Make one animal flat, iow, eliminate one, say, the turtle. When the cat is under the table, the distance from its head to the table top is 130. When it is on the table, the distance from its head to the floor is 170 ...

 

[Genady]

For a contrast, here is the ChatGPT's latest attempt:

 

Me:

 

There is a table and two boxes. When the small box is under the table and the large box is on the table, the distance between the top of the small box and the top of the large box is 170 cm. When the small box is on the table and the large box is under the table, the distance between the top of the large box and the top of the small box is 130 cm. How tall is the table? Solve without algebra, if possible.

 

ChatGPT:

Let's approach this problem without algebra and solve it using logical reasoning.

From the given information, we can determine that the distance between the top of the small box and the top of the large box is 170 cm when the small box is under the table and the large box is on the table. Similarly, when the small box is on the table and the large box is under the table, the distance between the top of the large box and the top of the small box is 130 cm.

Now, let's consider the scenario where the small box is under the table and the large box is on the table. The total height in this scenario would be the sum of the height of the small box and the height of the table. Thus, we have:

Height of small box + Height of table = 170 cm

Similarly, in the scenario where the small box is on the table and the large box is under the table, the total height would be the sum of the height of the large box and the height of the table. Therefore:

Height of large box + Height of table = 130 cm

Now, let's subtract the second equation from the first equation:

(Height of small box + Height of table) - (Height of large box + Height of table) = 170 cm - 130 cm

Height of small box - Height of large box = 40 cm

From this equation, we can deduce that the difference in height between the small box and the large box is 40 cm.

Since we want to find the height of the table, we can determine that the height of the table is equal to the difference in height between the two boxes, which is 40 cm.

Therefore, the height of the table is 40 cm.

 

[Genady]

Another fun puzzle that is too hard for AI:

[Genady]

Maybe this little puzzle (see above) got lost between a heated debate in the Politics forum and an endless blabbering in the Speculations forum, but for whatever reason nobody has replied to it yet. So, I've asked ChatGPT. Again. Twice. Here are its spectacularly nonsensical answers.

1.

To find the distance between the poles, we can use the Pythagorean theorem. Let's assume the distance between the poles is represented by "x."

We have a right triangle formed by the distance between the poles (x), the height of one pole (50 m), and the length of the cable (80 m).

The height of the lowest point of the cable (10 m) forms another right triangle with one of the poles (50 m) and the distance between the poles (x).

Using the Pythagorean theorem, we can set up the following equation:

x^2 + 10^2 = 50^2

Simplifying the equation:

x^2 + 100 = 2500

x^2 = 2400

Taking the square root of both sides:

x = √2400

x ≈ 48.99 m

Therefore, the poles are approximately 48.99 meters apart.

2.

To solve this problem, we can consider the triangle formed by the two poles and the center of the cable. Let's call the distance between the two poles "x".

We have a right triangle where one leg is the distance from the center of the cable to the ground (10 m), the other leg is half the distance between the two poles (x/2), and the hypotenuse is the cable itself (80 m).

Using the Pythagorean theorem, we can find the value of x:

(10)^2 + (x/2)^2 = 80^2

Simplifying the equation:

100 + (x/2)^2 = 6400

(x/2)^2 = 6300

Taking the square root of both sides:

x/2 = √6300

x/2 = 79.37

Multiplying both sides by 2:

x = 158.74

Therefore, the distance between the two poles is approximately 158.74 meters.

[TheVat]

4 hours ago, Genady said:

got lost between a heated debate in the Politics forum and an endless blabbering in the Speculations forum, but for whatever reason nobody has replied to it yet. 

Those forums have been distracting (and tedious to follow, so I gave up), so am glad you posted again. 

Spoiler

I think calculate half-period for a sine wave, for which we have amplitude of 40, and arc length of 80. 

I think this takes an elliptic integral and I haven't done that stuff in forty years, so maybe an easier way will present itself....

ChatGPT never fails to be amusing in its artificial stupidity.

 

 

[Genady]

42 minutes ago, TheVat said:

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maybe an easier way will present itself....

 

 

It will! 😉

Spoiler

Without algebra AND without calculus.

 

[TheVat]

Spoiler

Well, solve for a normal chord of parabola, but that would be algebra, so I guess it's even simpler.  Like that one earlier with bugs walking in a rotating shrinking rectangle.  I shall return.  We have torrential rain here, and some things to deal with.

 

[Genady]

3 hours ago, TheVat said:

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Like that one earlier with bugs walking in a rotating shrinking rectangle.

 

Spoiler

Yes, like that or simpler.

 

[TheVat]

Something a bit deceptive in that drawing.  LOL.  Yes, it is simple.

 

Spoiler

Very funny.  If the cable is 80m and poles are 50m, then placing poles side by side (zero distance) means each 40 meter half of cable goes straight down so it is 10 meters short of the ground.

 

[Genady]

3 minutes ago, TheVat said:

Something a bit deceptive in that drawing.  LOL.  Yes, it is simple.

 

  Reveal hidden contents

Very funny.  If the cable is 80m and poles are 50m, then placing poles side by side (zero distance) means each 40 meter half of cable goes straight down so it is 10 meters short of the ground.

 

Yes, just a bit... +1

BTW, ChatGPT didn't have this deception as the problem has been presented in a text. It didn't help.

[TheVat]

OpenAI should really think twice before releasing its stochastic parrots into the wild.   Not that it doesn't provide some amusement.  

Perhaps it will be remembered as the Magic 8-Ball of our time.

 

[Genady]

If Teresa's daughter is my daughter's mother, then what is my relationship to Teresa?

 

After you answer it, I will describe a little experiment with ChatGPT that sheds light on how it works.

[TheVat]

Mother-in-law.  I can well imagine a stochastic parrot would have trouble with that. 

[Genady]

Just now, TheVat said:

Mother-in-law.  I can well imagine a stochastic parrot would have trouble with that. 

You're right, of course, +1

But what kind of trouble...

At first, its answer was very impressive:

"If Teresa's daughter is your daughter's mother, then Teresa is your daughter's grandmother. Therefore, you are Teresa's son-in-law or daughter-in-law, depending on your gender."

Isn't it smart? Doesn't it demonstrate logical thinking abilities?

To see if it in fact does, I've substituted Teresa->John, daughter->son, and mother->father, and asked the same question in this form:

"If John's son is my son's father, then what is my relationship to John?"

And the ChatGPT's answer was:

"If John's son is your son's father, then John is your spouse or partner."

Why? What happened to the logic?

Of course, logic was never there. The "Teresa" form of the puzzle, verbatim, has been very popular on Internet several years ago. The search returns hundreds of thousands of links. So, it has been included in the ChatGPT training data. While for the "John" version all it could find was something about son, father, relationship... and all it could come up with was the stupid answer.

Yes, stochastic parrot is a correct definition.

 

 

[md65536]

On 6/11/2023 at 5:23 AM, Genady said:

If Teresa's daughter is my daughter's mother, then what is my relationship to Teresa?

There are several answers, but why wouldn't "You're Teresa's daughter" be the simplest assumption? It minimizes the number of people and relationships being talked about. "Mother in law" adds an assumption of marriage, which at least is a cultural bias an AI would need to be trained for.

[Genady]

40 minutes ago, md65536 said:

There are several answers, but why wouldn't "You're Teresa's daughter" be the simplest assumption? It minimizes the number of people and relationships being talked about. "Mother in law" adds an assumption of marriage, which at least is a cultural bias an AI would need to be trained for.

Why not? In fact, the original version of the puzzle was a multiple-choice, and the choices were:

I.e., originally, "Teresa's daughter" was the only correct answer.

[mistermack]

How would AI handle the simple ones ? 

An Englishman and an American are sitting on a wall. 

The Englishman is the father of the American's son.

Explain.