834725
Brain Teaser
Posts
Total:
89
-->
@ethang5
Hmm? ^
Nevermind rule 7
384725
boom
Nope 5
-->
@Speedrace
It's hard since Disc solved 1/2 of them too
492573
-->
@Vader
Rule 9
-->
@Speedrace
It follows all the rules but just been used
-->
@Vader
It has 3 consecutive odd numbers
-->
@Speedrace
No more than 3, it can have 3 numbers, not more than 3
-->
@Vader
It's hard since Disc solved 1/2 of them too
I have solved all of them, there is one that has not been posted yet.
Hint: It does not have a 9. I already posted 100% of the solutions that have 9s.
Other hint: The last solution does have an 8.
-->
@Discipulus_Didicit
Ptoeey. I don't like math anyway
-->
@Vader
Like zed said this isn't really math. This same exact puzzle could be replicated by replacing the numbers with letters.
If you can solve it before I get off work (7 hours) I will paypal you ten dollars.
-->
@Discipulus_Didicit
Now I am motivated
Are you sure?there is one that has not been posted yet.
Like zed said this isn't really math. This same exact puzzle could be replicated by replacing the numbers with letters.
What would rules #8 and #10 be like with letters?
-->
@ethang5
Are you sure?
Yes. If supa can't figure it out in the next 4 hours I will post it.
What would rules #8 and #10 be like with letters?
8 would be easy, just a short list of letters that are arbitrarily not allowed next to eachother (corresponding with all combinations of their respective numbers that are not allowed next to eachother)
Ex. "The following are not allowed next to eachother: B and D, B and F, B and H..." etc.
Rule 10 would be the same but with a longer list.
Ex. "The following three letter combinations may not be on the same side in any order..."
Much more complicated to write out and (at least for us humans) much harder to work with, but still technically doable.
-->
@Vader
Here is another hint:
492735 and 537249 are both valid answers.
357294 and 492753 are both valid answers.
Zed gave a valid answer on page one.
Neeeeeeerrrrrds.
-->
@Discipulus_Didicit
Are you sure?
Yes. If supa can't figure it out in the next 4 hours I will post it.
No, I meant, are you sure only one valid answer has not been posted?
just a short list of letters that are arbitrarily not allowed next to each other...
I would find that less interesting as the rules would be arbitrary instead of based on the mathematical relations between numbers.
Okay, the number 8 then.
Firstly the only set we can draw solutions from that contains an 8 is 234578. The set 234678 is invalid because it contains 4 even digits and even digits are not allowed to be adjacent. All other sets containing 8 are invalid due to rule 11.
So. 234578.
We start again with the truism that any solution containing 8 must have 8 in one of its 3 digit halves. The possible 3 digit halves list starts a bit larger than when we worked with 9 because rule 10 is less restrictive on 8 than it is on 9:
238
248
258
348
Four starting possibilities rather than two as there were for 9 yet we already know that there are more solutions with 9 than with 8. I suspect the filter will be when we start applying rule 8 in earnest, as 8 has more factors than 9. In fact we can already see this when we remove the '248' pattern due to it containing all even numbers.
After removing the 248 pattern we go to expand upon the permutations of the remaining patterns. Each has exactly one odd number which must be kept in the middle to seperate the two even numbers. Thus we have:
238
832
258
852
438
834
Of course rule 7 cuts most of these out immediately and we are left with:
258
852
Remember that the only set we can work with is 234578. At this point I get the idea for a little shortcut. Because we have only one set to work with let's put the 8 side on hold for a moment and look at what the other side must look like. Firstly we know its numbers must be 3, 4, and 7. The three and 4 cannot be adjacent however so we have only 374 and 473 as possibilities for the other side.
So one side must be 258 or 852 and the other muat be 374 or 473. The only legal ways to "glue" these two sides together are as follows:
258374
473852
And thus we have our only two possible solutions containing an 8. One of them was already posted by zed and the other is just the mirror opposite. A bit disappointing then that we found no new solutions (we already knew that the mirror opposite of any valid solution is itself a valid solution) but it still serves as a logical proof that no such new solutions exist so at least we know not to keep looking for more, this is all there is.
-->
@ethang5
I would find that less interesting as the rules would be arbitrary instead of based on the mathematical relations between numbers.
Hard to disagree with that.
-->
@ethang5
No, I meant, are you sure only one valid answer has not been posted?
I understood the question. My answer was yes. It is possible that I am mistaken though. Has anyone said 258374?
-->
@Discipulus_Didicit
Nope. 258374 - Submitted by DD
Just double chacked. 258374 was not said yet at the time I said "the last solution has not been posted yet"
As noted in post 81 the fact that it is the mirror of zeds answer makes it less original (and probably the source of your confusion, I suspect you already knew that the mirror of any valid solution is valid and seeing zeds answer just subconsciously regustered with you as both answers for that reason) but still technically new.
-->
@ethang5
All solutions have now been registered as proved in my 2 bigger posts. This was a very fun thread, thanks for making it!
-->
@Zaradi
But after we come up with the digital chip that allows you to post on the internet, you will have forgotten that you're standing on the shoulders of Neeeeeeerrrrrds.
You're still welcome. The world will always need clerks.
Actually I never posted the proof that 234567 is not a valid set but I did run through the proof myself (and double checked it after I noticed my rule 8 interpretation error) and it is very much an invalid set.
-->
@Discipulus_Didicit
Much of it's enjoyment was your posts. Thanks too.