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# Maths in bed - Latin square

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1. I'm sat in bed working through some puzzles and I can't do this...anyone have any ideas??

2. A diff one I tried -

Using the info I had, I filled in the certain boxes with every number they could possibly have in them...it didn't help
3. ...this is the last kind of thing i'd want to be doing.
4. (Original post by ihatePE)
...this is the last kind of thing i'd want to be doing.
It's great fun....the feeling when you finally figure it out tho

I want that feeeeeeeling but I can't do it 😩
5. I'd help

But not at this time
6. What book is this??
7. (Original post by Biryani007)
A diff one I tried -

Using the info I had, I filled in the certain boxes with every number they could possibly have in them...it didn't help
Post it in Maths
8. (Original post by Lord Samosa)
I'd help

But not at this time
Maths at night is the best <333

(Original post by TheonlyMrsHolmes)
What book is this??
It's a brain training book I picked up from Aldi...most of the questions I've done were pretty straight forward imo...just this one has left me confuzzled

(Original post by M14B)
Post it in Maths
Good idea..

iEthan can this thread be moved to Maths or will I have to make another thread?
9. I think you have be changing the numbers (if you have to) sometimes so that the equation at the top are true.

So the first one is A345=11 so A3, A4, A5 are three numbers that add up to 11.

So you can have 5+5+1, 7+3+1 (etc) in boxes A3, A4, A5.

Spoiler:
Show
though I could be wrong, it is 7:30am after all
10. Is it even possible? If we have a 6x6 matrix :

And CD3=11,(I'm assuming this means C3 +D3 =11), then , since it must be less than 6 then and , but D456 =6, meaning , this restricts it so that

but, there is no number for:
and

Or maybe I'm reading it wrong.
11. NotNotBatman You need a different Latin square.

Biryani007

D E 1=11. This covers two squares and the only combination of two numbers is 5 and 6. Implying .

We can also infer that 5,6 cannot be in A1,B1,C1,F1.

D 4 5 6 =6. Three integers that are all different that add to 6, can only be 1,2,3 etc.

Final Solution:
Spoiler:
Show

142563
356412
425631
514326
263154
631245

12. (Original post by ghostwalker)
NotNotBatman You need a different Latin square.

Biryani007

D E 1=11. This covers two squares and the only combination of two numbers is 5 and 6. Implying .

We can also infer that 5,6 cannot be in A1,B1,C1,F1.

D 4 5 6 =6. Three integers that are all different that add to 6, can only be 1,2,3 etc.

Final Solution:
Spoiler:
Show

142563
356412
425631
514326
263154
631245

In my second post I uploaded a pic of one I tried...I did what you did and found all the possible numbers you could have in the boxes mentioned...it doesn't make it any clearer...how would you know what order the numbers go in the squares? Just trial and error after you've narrowed it down or is there a method?

(Original post by NotNotBatman)
Is it even possible? If we have a 6x6 matrix :

And CD3=11,(I'm assuming this means C3 +D3 =11), then , since it must be less than 6 then and , but D456 =6, meaning , this restricts it so that

but, there is no number for:
and

Or maybe I'm reading it wrong.
Is that how you do it? Using one of those squares with letters filled in?

(Original post by aamirac)
I think you have be changing the numbers (if you have to) sometimes so that the equation at the top are true.

So the first one is A345=11 so A3, A4, A5 are three numbers that add up to 11.

So you can have 5+5+1, 7+3+1 (etc) in boxes A3, A4, A5.
Spoiler:
Show
though I could be wrong, it is 7:30am after all
I did that but there's a load of possibilities, and they could be in any order
13. (Original post by ghostwalker)
NotNotBatman You need a different Latin square.

Biryani007

D E 1=11. This covers two squares and the only combination of two numbers is 5 and 6. Implying .

We can also infer that 5,6 cannot be in A1,B1,C1,F1.

D 4 5 6 =6. Three integers that are all different that add to 6, can only be 1,2,3 etc.

Final Solution:
Spoiler:
Show

142563
356412
425631
514326
263154
631245

So, would a systematic trial and error method need to be used, since there are many matrices that are orthogonal to the one I wrote? Or is there another method?

(Original post by Biryani007)
Is that how you do it? Using one of those squares with letters filled in?
Well I tried doing that, but now, I think it's very impractical, as there are too many 6x6 latin squares to know which one to use.
14. (Original post by Biryani007)
In my second post I uploaded a pic of one I tried...I did what you did and found all the possible numbers you could have in the boxes mentioned...it doesn't make it any clearer...how would you know what order the numbers go in the squares? Just trial and error after you've narrowed it down or is there a method?
There's no formal method that I'm aware of. Just see what's the next step. What can you deduce from your current information.

D345=6. So, these must be 1,2,3 in some order.

It follows that D1,D2,D6 are each one of 4,5,6.

But DE1=5, So, D1,E1 are at most 4, hence D1=4.

And, D2, D6 are now 5 or 6.

DE1=5. Since D1 is now 4, then E1=1

It's a bit like Sudoku, and a lot of other logic games.

Edit: Corrected.
15. (Original post by NotNotBatman)
So, would a systematic trial and error method need to be used, since there are many matrices that are orthogonal to the one I wrote? Or is there another method?
I wouldn't use matrices.

Logical deduction is the way to go, IMO.
16. (Original post by ghostwalker)
There's no formal method that I'm aware of. Just see what's the next step. What can you deduce from your current information.

D345=6. So, these must be 1,2,3 in some order.

It follows that D1,D2,D6 are each one of 4,5,6.

But DE2=5, So, D2,E2 are at most 4, hence D2=4.

And, D1, D6 are now 5 or 6.

DE2=9. Since D2 is now 4, then E2=5

It's a bit like Sudoku, and a lot of other logic games.
I get that it's done logically...it's placing the initial numbers that's stopping me really...the 1,2,3 do I place in any order and then change up if I need to later on? D3 has an equal chance of being 1, 2 or 3 right? My question was how do I know which of those it is for my initial squares?
17. (Original post by Biryani007)
I get that it's done logically...it's placing the initial numbers that's stopping me really...the 1,2,3 do I place in any order and then change up if I need to later on? D3 has an equal chance of being 1, 2 or 3 right? My question was how do I know in what order to place them..
You don't. You put 1,2,3 in each of the three cells. Then as more information becomes available you can start crossing out.

You'll find you have to run through the given clues numerous times. You need to maximise what you can deduce. E.g. If DE3=7, and D3 has {1,3,4} in it, then E3 can only have {6,3,4}

Sometimes the next step is obvious, sometimes it's incredibly difficult.
18. (Original post by ghostwalker)
You don't. You put 1,2,3 in each of the three cells. Then as more information becomes available you can start crossing out.

You'll find you have to run through the given clues numerous times. You need to maximise what you can deduce. E.g. If DE3=7, and D3 has {1,3,4} in it, then E3 can only have {6,3,4}

Sometimes the next step is obvious, sometimes it's incredibly difficult.
Eurgh I hate how confused I am

Ive done that for all the boxes I can in post 2...looking at that what would your next step be?

Sorry
19. (Original post by Biryani007)
Eurgh I hate how confused I am

Ive done that for all the boxes I can in post 2...looking at that what would your next step be?

Sorry
Looks as if you don't have any squares finalised there. See my post #14. It had a massive error, so you can't have read it. Corrected now.
20. (Original post by ghostwalker)
Looks as if you don't have any squares finalised there. See my post #14. It had a massive error, so you can't have read it. Corrected now.
Ahh yeah I think I've got it now...so 1,2,3 you wont have finalised yet because you cant...that'll be done with info later on, right?

For other squares, how'd you pick a good place to start...clues that cover the most squares and then work in the column/row around it like you did for this one...coz I'm guessing starting anywhere wouldn't really work?

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