2

[Hawkeye]

And there is a solution to the one I posed. Want a hint? I did not put the answer.

Spoiler

Not all the intermediate steps are whole numbers.

hurray for reverse engineering

This is the only way I got it.

 

[Trebuchet]

Your spoiler is correct for x squared plus two equal three cubed, but here is the puzzle. That is the ONLY solution. Apparently there is no easy way to prove that. It's advanced number theory and I don't know how.

For the 5,5,5,1 I have only 5*5-1 = 24 or 5*5-(1 to the 5th) = 24. Don't know any fractional solution.

Your answer is an excellent one. When I solved it, I didn't consider powers since it was in the set up that they weren't allowed, so I hadn't thought of that. I didn't say it explicitly, but since the order of operations is up to you, parentheses must be allowed, too.

Next hint, then:

Spoiler

What is 24/5?

 

[BigApplePi]

hurray for reverse engineering

This is the only way I got it.

Didn't do me a bit of good.

 

[BigApplePi]

Your answer is an excellent one. When I solved it, I didn't consider powers since it was in the set up that they weren't allowed, so I hadn't thought of that. I didn't say it explicitly, but since the order of operations is up to you, parentheses must be allowed, too.

Next hint, then:

Spoiler

What is 24/5?

Now if one gets the answer from the clue, how does one explain not getting it wo the clue? Lack of organizational thinking?

If I can miss this one, does this mean WE have missed something explaining quantum mechanics and there is an equally hidden answer?

 

[BigApplePi]

BigApplePi
For the 5,5,5,1 problem of getting 24 I have only 5*5-1 = 24 or 5*5-(1 to the 5th) = 24. Don't know any fractional solution.

For those who got the answer to this problem, I did not though I have it now. Since I have a degree in math, how do you explain that? Have you ever had a mental block? As the problem was presented, there were certain restrictions. I forgot about them and thought only of + - * /. I shut out parentheses. Now I know perfectly well what ( ) are. I just shut out the idea. As soon as one allows ( ), the solution is easy. Ever happened to you? It must be like writer's block. It must be what an unconscious bias is.

 

[Trebuchet]

For those who got the answer to this problem, I did not though I have it now. Since I have a degree in math, how do you explain that? Have you ever had a mental block? As the problem was presented, there were certain restrictions. I forgot about them and thought only of + - * /. I shut out parentheses. Now I know perfectly well what ( ) are. I just shut out the idea. As soon as one allows ( ), the solution is easy. Ever happened to you? It must be like writer's block. It must be what an unconscious bias is.

I would offer the explanation that since I didn't mention parentheses, and I listed + - * and / as the only operations allowed, you shut them out of your solution space. I'd say it was the problem statement, since once you knew parentheses were allowed, you got it.

 

[BigApplePi]

I would offer the explanation that since I didn't mention parentheses, and I listed + - * and / as the only operations allowed, you shut them out of your solution space. I'd say it was the problem statement, since once you knew parentheses were allowed, you got it.

What I find interesting here beside the math'l problem is the failure to find a solution when a solution exists. Do you know the story of Archimedes who was assigned the task of determining if the king's crown was pure gold or not? He couldn't solve the problem either. Then one day sitting in his bath a bright idea came to him. He was so excited he ran into the streets of Athens naked shouting "Eureka! Eureka!" I have found it. I have found it.

 

[Hawkeye]

if in doubt, have a shave with Occam's Razor.

 

[BigApplePi]

if in doubt, have a shave with Occam's Razor.

What's that? I've heard of it.

 

[Hawkeye]

Basically it means 'don't try to make something more complicated than it actually is'.

 

[BigApplePi]

Basically it means 'don't try to make something more complicated than it actually is'.

Yeah but that's nearly impossible. When people attack a problem, scientists say, they have to try lots of things, make lots of errors and if they stumble on a solution then they have gone on quite a circuitous path. So they have to clean up their act before they announce their solution.

Consider Fermat's Last Theorem. If I recall it took hundreds of pages of proof. Who want's that? Hardly something to please an intuitive if one happens to be an xNTx, lol.

Or did I misunderstand what you said?

 

[Geminii]

Re: 7. Have you tried comparing that technique with basic long division?

It pretty much is long division, yes. It's just presented in a way to make it easier to do in large visual chunks.

And hey, I've come up with worse stuff in ten minutes before!

 

[walfin]

I realise nobody gave the 1729 answer (taxicab hint notwithstanding - actually I don't really understand that hint).

Very well, the first answer is 1728+1 (I've got the other answer too; I didn't google for this, just knew it intuitively)

Also, have you realized there are two arguments for the addition function? There's a hint.

I already said this earlier.

Basically it means 'don't try to make something more complicated than it actually is'.

Actually it didn't work for me either, took me a while to get it.

The 1^5 solution was easier.

 

[BigApplePi]

I realise nobody gave the 1729 answer (taxicab hint notwithstanding - actually I don't really understand that hint).

Very well, the first answer is 1728+1 (I've got the other answer too; I didn't google for this, just knew it intuitively)


I already said this earlier.


Actually it didn't work for me either, took me a while to get it.

The 1^5 solution was easier.

Good. That is one of the answers because 12 cubed = 1728 & 1 cubed = 1. The taxicab hint refers to a mathematician when challenged that the number on a taxicab was interesting or not, remarked it (1729) was the sum of two cubes in two different ways. Therefore it WAS interesting. I don't recall if it was supposed to be the ONLY number like that.