Brain Teaser

Author: ethang5
Puzzle
Brain
Math

Posts

Total: 89
#31
Discipulus_Didicit
Discipulus_Didicit's avatar
Debates: 9
Posts: 5,758
3
4
10
Discipulus_Didicit's avatar
Discipulus_Didicit
3
4
10
-->
@ethang5
We can further rule out any solution containing a 9*
Are you sure? 

No I am not lol. Gimmie aboit a half hour to double check my proof on that (multitasking at the moment, trying to file taxes).
Topic's author
#32
ethang5
ethang5's avatar
Debates: 1
Posts: 5,875
3
3
6
ethang5's avatar
ethang5
3
3
6
-->
@Discipulus_Didicit
You're right, it violates rule 7 but not 10.

And I edited the post concerning rule 8.

#33
zedvictor4
zedvictor4's avatar
Debates: 22
Posts: 12,067
3
3
6
zedvictor4's avatar
zedvictor4
3
3
6
-->
@ethang5
A few minutes.

Most of the time was taken up by checking that I hadn't infringed the rules.

Concentrating on rule 10 was the key.
#34
Discipulus_Didicit
Discipulus_Didicit's avatar
Debates: 9
Posts: 5,758
3
4
10
Discipulus_Didicit's avatar
Discipulus_Didicit
3
4
10
-->
@ethang5
Oh okay "in your other musings" makes sense and is true.

Rule 8 was actually on the forefront of my mind for much of the time and was key to many of the promised "explanations" that I did not go into detail about but drew conclusions from (the ones with a * next to them). I just didn't go into detail on all of them due to time constraints. I am currently making a post that details my conclusion that no 9s can be used, in part to check whether there was a flaw in my reasoning there.
#35
Discipulus_Didicit
Discipulus_Didicit's avatar
Debates: 9
Posts: 5,758
3
4
10
Discipulus_Didicit's avatar
Discipulus_Didicit
3
4
10
Stream of consciousness here, might be hard to follow this post despite the simplicity of its its concepts due to lack of good formatting on my part. You have been warned

So... As to whether there can be any 9s...

Any solution with a 9 would have to have the 9 on one of the sides (truism).

The only possible 3 digit combinations for the 9 that could appear on one of the halves of the solution would have to be some combination from the set of 239 or 249. This is because 1 and 0 cannot be used and any other 3 digit set would violate rule 6 or 10.

2 cannot be adjacent to 3 (rule 7) or 4 (rule 5) so in both these scenarios 9 would have to be the second number of the 3 digit set to seperate the 2 from the other number.

This leaves us with:

293
392
294
492

9 and 3 cannot be adjacent though (rule 5) so we are left with:

294
492

These patterns must appear in any proposed solution with a 9. Can these patterns be ruled out?

In both cases the border of the other 3 digit set is an even number (2 or 4) and an even number cannot be adjacent to another even number (rule 8) so the next digit has to be odd. This leaves us with only 5 or 7 as the candidates for the first digit of the next 3 digit set (because rule 6 and 7 and excluding the number 1)

So now we know any solution containing a 9 must have this pattern of 4 digits:

2945
4927
2947
4925

But rule 7 once again comes in to spoil the fun, leaving us with:

4927
2947
4925

Now let us look at remaining possibilities for the last 2 digits. Looking just at rule 6 we see that what we have to work with is this:

3 (5) 6 (7) 8

Parenthesis indicate numbers available in some of our partly-constructed solutions but not all.

Looking over these numbers we see 8 is excluded from filling out all our partial solutions due to rule 10. So...

3 (5) 6 (7)

All but one of these are odd numbers so we must be careful now of rule 9. In fact because of rule 9 the 6 MUST be used as one of the 2 final digits. The remaining possibilities are thus:

4927_6
2947_6
4925_6
49276_
29476_
49256_

All other iterations have been ruled out unless I made some mistake and the digits permitted to fill these blanks are:

3 (5) (7)

Except 3 and 6 cannot be adjacent (rule 8) so actually we can only fill each of these blanks with a 5 or 7, depending on which does not violate rule 6 for each possibility.

So now...

492756
294756
492576
492765
294765
492567

All of these violate rule 10.

Therefore unless I screwed something up 9 cannot exist in any possible solution.
#36
Discipulus_Didicit
Discipulus_Didicit's avatar
Debates: 9
Posts: 5,758
3
4
10
Discipulus_Didicit's avatar
Discipulus_Didicit
3
4
10
-->
@ethang5
See above post. During the hour and a half or so I spent on post 16 I did most of the proof of "9 not being in any solution" in my head due to time constraints so I was not 100% sure that the conclusion was accurate. Now that I have written out the proof in detail though I am confident that I was correct in this conclusion.
Topic's author
#37
ethang5
ethang5's avatar
Debates: 1
Posts: 5,875
3
3
6
ethang5's avatar
ethang5
3
3
6
-->
@zedvictor4
A few minutes
Impressive. Do you consider yourself good at math?

Concentrating on rule 10 was the key.
Yeah, going in I thought rules 8 and 10 would be the most tricky.
Topic's author
#38
ethang5
ethang5's avatar
Debates: 1
Posts: 5,875
3
3
6
ethang5's avatar
ethang5
3
3
6
-->
@Discipulus_Didicit
 How about 294735?
#39
Discipulus_Didicit
Discipulus_Didicit's avatar
Debates: 9
Posts: 5,758
3
4
10
Discipulus_Didicit's avatar
Discipulus_Didicit
3
4
10
-->
@ethang5
Rule 9.
#40
Discipulus_Didicit
Discipulus_Didicit's avatar
Debates: 9
Posts: 5,758
3
4
10
Discipulus_Didicit's avatar
Discipulus_Didicit
3
4
10
Wait
#41
Discipulus_Didicit
Discipulus_Didicit's avatar
Debates: 9
Posts: 5,758
3
4
10
Discipulus_Didicit's avatar
Discipulus_Didicit
3
4
10
-->
@ethang5
Okay so THIS ENTIRE TIME I thought rule 9 was "cannot have 3 or more consecutive odd numbers"

I am ONLY JUST NOW realizing that it is "cannot have more than three consecutive odd numbers"

So three odds in a row are allowed.

So... I have been making my job orders of magnitude more difficult for no reason.

You have no idea how much of a pain in my ass this incorrect interpratation of rule 9 has been lmao.

🤦 Classic DD fail.
#42
Discipulus_Didicit
Discipulus_Didicit's avatar
Debates: 9
Posts: 5,758
3
4
10
Discipulus_Didicit's avatar
Discipulus_Didicit
3
4
10
-->
@ethang5
Going by my (incorrect) interpratation of rule 9 there can be no 9s. Now that I know that interpratation was incorrect though this puzzle becomes many times easier in SO MANY ways.
#43
zedvictor4
zedvictor4's avatar
Debates: 22
Posts: 12,067
3
3
6
zedvictor4's avatar
zedvictor4
3
3
6
-->
@ethang5
Well my math is fine.

Though there was no complex math required with that problem.

It was simply about sequencing digits relative to certain criteria.

I like to do number puzzles, sudoku etc. maybe that helps.
#44
Discipulus_Didicit
Discipulus_Didicit's avatar
Debates: 9
Posts: 5,758
3
4
10
Discipulus_Didicit's avatar
Discipulus_Didicit
3
4
10
Let's see...

492735
492753
492537
492573
294735
294753
735294
537294
537492
357294
357492
375294

These should be all the possible solutions containing 9s (based mostly on my work in post 35 so it was not all in vain)!

Easy to come up with now that I know I was misreading the rules this whole time lmao.
#45
Discipulus_Didicit
Discipulus_Didicit's avatar
Debates: 9
Posts: 5,758
3
4
10
Discipulus_Didicit's avatar
Discipulus_Didicit
3
4
10
-->
@Vader
This also means supa had a correct solution in post 24. I told him in post 25 that it was incorrect based on rule 9 but that was an incorrect interpratation of rule 9, supa actually didn't break any rules with that one.
Topic's author
#46
ethang5
ethang5's avatar
Debates: 1
Posts: 5,875
3
3
6
ethang5's avatar
ethang5
3
3
6
-->
@Discipulus_Didicit
No. Your musings were interesting, and they were logical given your belief. You also pointed out things I had not thought of.

You would make a great math teacher.


Topic's author
#47
ethang5
ethang5's avatar
Debates: 1
Posts: 5,875
3
3
6
ethang5's avatar
ethang5
3
3
6
-->
@Vader
@Discipulus_Didicit
All your answers in post #44 are keerect! You hold the title of most correct answers.

This also means supa had a correct solution in post 24. I told him in post 25 that it was incorrect based on rule 9 but that was an incorrect interpratation of rule 9, supa actually didn't break any rules with that one.
But we will never know if he figured it out or simply guessed. But a correct answer is a correct answer.

Supa is on board!
Topic's author
#48
ethang5
ethang5's avatar
Debates: 1
Posts: 5,875
3
3
6
ethang5's avatar
ethang5
3
3
6
-->
@Vader
@zedvictor4
@Discipulus_Didicit
Correct answers so far.

473852 - Submitted by Zed    *first
492735 - Submitted by Supa
294735 - Submitted by Ethan

 * del *   492753  492537
492573  294735  294753
735294  537294  537492
357294  357492  375294
Submitted by Discipulus_Didicit   *most
Topic's author
#49
ethang5
ethang5's avatar
Debates: 1
Posts: 5,875
3
3
6
ethang5's avatar
ethang5
3
3
6
Only one correct answer so far with an 8.
#50
Discipulus_Didicit
Discipulus_Didicit's avatar
Debates: 9
Posts: 5,758
3
4
10
Discipulus_Didicit's avatar
Discipulus_Didicit
3
4
10

You also pointed out things I had not thought of.

You would make a great math teacher.

Eh, it is usually helpful to get multiple points of view. Someone somewhere will usually think of something you don't. Occasionally they will even think of something that actually makes sense. Not sure I would make a great teacher though. I'm a lot better at learning lol.

 * del *   492753  492537
492573   * del *   294753
735294  537294  537492
357294  357492  375294
Submitted by Discipulus_Didicit   *most

I think the one you gave me should be removed too.

Anyway I have listed all solutions that have 9s in them. Finding the remaining solutions is as simple as just taking 8 and 7 and doing the same thing to them that I did to 9 earlier (no need to do this to any other numbers as all solutions must have at least a 7 or 8 or 9 due to the combination of rules 1, 4, 6, and 8).

I won't do this right now though. If nobody else has by tonight or tomorrow then I might but not right away, I will let someone else have a chance ;-)
Topic's author
#51
ethang5
ethang5's avatar
Debates: 1
Posts: 5,875
3
3
6
ethang5's avatar
ethang5
3
3
6
Finding the remaining solutions is as simple as just taking 8 and 7 and doing the same thing to them that I did to 9 
It will be much harder for 8 than for 7. For some reason, odd numbers do not behave like the mirror image of even numbers.

Someone somewhere will usually think of something you don't. Occasionally they will even think of something that actually makes sense.
Good at math, and not conceited, and a wry sense of humor? It's going to be bittersweet to shoot down another of your arguments when the time comes.
#52
Discipulus_Didicit
Discipulus_Didicit's avatar
Debates: 9
Posts: 5,758
3
4
10
Discipulus_Didicit's avatar
Discipulus_Didicit
3
4
10
-->
@ethang5
For some reason, odd numbers do not behave like the mirror image of even numbers.

Rule 8 is that reason. Evens all have multiples with eachother. Most of the odds we are working with are prime numbers with no multiples at all.

Good at math, and not conceited, and a wry sense of humor?

I am good at math and my sense of humor is pretty wry. You got two out of three correct, not bad 👍

It's going to be bittersweet to shoot down another of your arguments when the time comes.

Sure, sure. Find something besides religion that we disagree on (my interest in that topic waxes and wanes over time, currently moreso the waning than the waxing) and I'll be happy to oblige to you making such an attempted shoot-down.
#53
Vader
Vader's avatar
Debates: 30
Posts: 14,984
5
8
11
Vader's avatar
Vader
5
8
11
835274

#54
Vader
Vader's avatar
Debates: 30
Posts: 14,984
5
8
11
Vader's avatar
Vader
5
8
11
Nevermind that one
#55
Vader
Vader's avatar
Debates: 30
Posts: 14,984
5
8
11
Vader's avatar
Vader
5
8
11
294735

#56
Vader
Vader's avatar
Debates: 30
Posts: 14,984
5
8
11
Vader's avatar
Vader
5
8
11
And Disc took that one

#57
Vader
Vader's avatar
Debates: 30
Posts: 14,984
5
8
11
Vader's avatar
Vader
5
8
11
285374

#58
Vader
Vader's avatar
Debates: 30
Posts: 14,984
5
8
11
Vader's avatar
Vader
5
8
11
Never mind that one tooo, Smdh
#59
Vader
Vader's avatar
Debates: 30
Posts: 14,984
5
8
11
Vader's avatar
Vader
5
8
11
258735
#60
Vader
Vader's avatar
Debates: 30
Posts: 14,984
5
8
11
Vader's avatar
Vader
5
8
11
Not that one, either, ugggg