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-4 to 4 puzzle combos
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Posted on: Sun Feb 09, 2020 12:01 am

Posts: 81
Joined: Tue Apr 24, 2012 7:47 pm
-4 to 4 puzzle combos
A little over two months ago, beaker had been struggling with a -1 to 4 bonus puzzle which went unsolved due to lack of a table. Several years ago, I myself had a -2 to 3 puzzle (IIRC) that I let go of for the same reason. That said, I present you with tables for -4 to 4 puzzles. First, though, there are 3 major things to watch out for:

A) These tables ONLY include -4 to 4 inclusive
B) I did NOT include cages with 4 or more cells
C) I ONLY included combos for addition and subtraction

I've been reading in the forum that there are different "flavors" of puzzles involving negative numbers. -1 to 3? Voila, you're covered! -2 to 4? You're good to go! -3 to 3? Bingo! -4 to 1? Bada bing, bada boom, everything's hunky dory! -5 to 7? Well..... unfortunately, no, I cannot help with THAT (not completely, anyhow). At any rate, though, I hope you enjoy and are helped by these tables.

skeeter84

2 cell subtraction

-8: [-4, 4]
-7: [-4, 3]; [-3, 4]
-6: [-4, 2]; [-3, 3]; [-2, 4]
-5: [-4, 1]; [-3, 2]; [-2, 3]; [-1, 4]
-4: [-4, 0]; [-3, 1]; [-2, 2]; [-1, 3]; [0, 4]
-3: [-4, -1]; [-2, 1]; [-3, 0]; [-1, 2]; [0, 3]; [1, 4]
-2: [-4, -2]; [-3, -1]; [-2, 0]; [-1, 1]; [0, 2]; [1, 3]; [2, 4]
-1: [-4, -3]; [-3, -2]; [-2, -1]; [-1, 0]; [0, 1]; [1, 2]; [2, 3]; [3, 4]
1: [-3, -4]; [-2, -3]; [-1, -2]; [0, -1]; [1, 0]; [2, 1]; [3, 2]; [4, 3]
2: [-2, -4]; [-1, -3]; [0, -2]; [1, -1]; [2, 0]; [3, 1]; [4, 2]
3: [-1, -4]; [0, -3]; [1, -2]; [2, -1]; [3, 0]; [4, 1]
4: [0, -4]; [1, -3]; [2, -2]; [3, -1]; [4, 0]
5: [1, -4]; [2, -3]; [3, -2]; [4, -1]
6: [2, -4]; [3, -3]; [4, -2]
7: [3, -4]; [4, -3]
8: [4, -4]

-7: [-4, -3]
-6: [-4, -2]
-5: [-4, -1]; [-3, -2]
-4: [-4, 0]; [-3, -1]
-3: [-4, 1]; [-3, 0]; [-2, -1]
-2: [-4, 2]; [-3, 1]; [-2, 0]
-1: [-4, 3]; [-3, 2]; [-2, 1]; [-1, 0]
0: [-4, 4]; [-2, 2]; [-3, 3]; [-1, 1]
1: [-3, 4]; [-2, 3]; [-1, 2]; [0, 1]
2: [-2, 4]; [-1, 3]; [0, 2]
3: [-1, 4]; [0, 3]; [1, 2]
4: [0, 4]; [1, 3]
5: [1, 4]; [2, 3]
6: [2, 4]
7: [3, 4]

3 cell subtraction

12: [4, -4, -4]
11: [3, -4, -4]; [4, -4, -3]
10: [2, -4, -4]; [3, -3, -4]; [4, -3, -3]; [4, -4, -2]
9: [1, -4, -4]; [2, -4, -3]; [3, -2, -4]; [3, -3, -3]; [4, -3, -2]; [4, -4, -1]

8: [0, -4, -4]; [1, -3, -4]; [2, -3, -3]; [2, -2, -4]; [3, -3, -2]; [3, -1, -4]; [4, -3, -1];
[4, -4, 0]; [4, -2, -2]

7: [-1, -4, -4]; [0, -3, -4]; [1, -3, -3]; [1, -2, -4]; [2, -2, -3]; [2, -1, -4]; [3, -2, -2];
[3, -3, -1]; [3, -4, 0]; [4, -3, 0]; [4, -4, 1]; [4, -2, -1]

6: [-2, -4, -4]; [-1, -3, -4]; [0, -2, -4]; [0, -3, -3]; [1, -1, -4]; [1, -2, -3]; [2, -3, -1];
[2, -4, 0]; [2, -2, -2]; [3, -3, 0]; [3, 1, -4]; [3, -2, -1]; [4, -3, 1]; [4, -4, 2];
[4, -1, -1]; [4, -2, 0]

5: [-3, -4, -4]; [-2, -3, -4]; [-1, -2, -4]; [-1, -3, -3]; [0, -1, -4]; [0, -2, -3]; [1, -4, 0];
[1, -1, -3]; [1, -2, -2]; [2, -3, 0]; [2, -2, -1]; [2, 1, -4]; [3, -3, 1]; [3, -1, -1];
[3, -2, 0]; [3, 2, -4]; [4, -3, 2]; [4, -4, 3]; [4, -1, 0]; [4, -2, 1]

4: [-3, -3, -4]; [-2, -3, -3]; [-2, -2, -4]; [-1, -2, -3]; [-1, -1, -4]; [0, -2, -2]; [0, -3, -1];
[0, 0, -4]; [1, -3, 0]; [1, -1, -2]; [1, 1, -4]; [2, -3, 1]; [2, -1, -1]; [2, -2, 0];
[2, 2, -4]; [3, -3, 2]; [3, -1, 0]; [3, -2, 1]; [3, 3, -4]; [4, 2, -2]; [4, 1, -1];
[4, 0, 0]; [4, 3, -3]; [4, 4, -4]

3: [-4, -4, -3]; [-3, -4, -2]; [-2, -2, -3]; [-2, -1, -4]; [-1, -2, -2]; [-1, -4, 0]; [-1, -1, -3];
[0, -1, -2]; [0, 1, -4]; [0, 0, -3]; [1, -1, -1]; [1, -2, 0]; [1, 2, -4]; [1, 1, -3];
[2, -1, 0]; [2, -2, 1]; [2, 2, -3]; [2, 3, -4]; [3, 0, 0]; [3, 4, -4]; [3, 3, -3];
[3, 2, -2]; [3, 1, -1]; [4, 2, -1]; [4, 1, 0]; [4, 3, -2]; [4, 4, -3]

2: [-4, -4, -2]; [-4, -3, -3]; [-3, -3, -2]; [-3, -1, -4]; [-2, -4, 0]; [-2, -3, -1]; [-1, -3, 0];
[-1, 1, -4]; [-1, -1, -2]; [0, -1, -1]; [0, 2, -4]; [0, 1, -3]; [0, 0, -2]; [1, -1, 0];
[1, 3, -4]; [1, 2, -3]; [1, 1, -2]; [2, 0, 0]; [2, 4, -4]; [2, 3, -3]; [2, 2, -2];
[2, 1, -1]; [3, -3, 4]; [3, 1, 0]; [3, 2, -1]; [3, 3, -2]; [4, 2, 0]; [4, 1, 1];
[4, 4, -2]; [4, 3, -1]

1: [-4, -4, -1]; [-4, -3, -2]; [-3, -4, 0]; [-3, -3, -1]; [-3, -2, -2]; [-2, -3, 0]; [-2, -2, -1];
[-2, 1, -4]; [-1, -2, 0]; [-1, 2, -4]; [-1, 1, -3]; [0, 3, -4]; [0, 2, -3]; [0, 1, -2];
[0, 0, -1]; [1, 0, 0]; [1, 4, -4]; [1, 3, -3]; [1, 2, -2]; [1, 1, -1]; [2, -3, 4];
[2, -2, 3]; [2, 2, -1]; [2, 1, 0]; [3, 3, -1]; [3, 2, 0]; [3, 1, 1]; [3, 4, -2];
[4, 2, 1]; [4, 4, -1]; [4, 3, 0]

0: [-4, -4, 0]; [-4, -3, -1]; [-4, -2, -2]; [-3, -3, 0]; [-3, -2, -1]; [-3, 1, -4]; [-2, -3, 1];
[-2, -1, -1]; [-2, -2, 0]; [-2, 2, -4]; [-1, 2, -3]; [-1, 1, -2]; [-1, -1, 0]; [-1, 3, -4];
[0, 3, -3]; [0, 2, -2]; [0, 1, -1]; [0, 4, -4]; [1, -1, 2]; [1, -2, 3]; [1, -3, 4];
[1, 1, 0]; [2, -2, 4]; [2, 3, -1]; [2, 2, 0]; [2, 1, 1]; [3, -1, 4]; [3, 3, 0];
[3, 2, 1]; [4, 2, 2]; [4, 4, 0]; [4, 3, 1]

-1: [-4, -4, 1]; [-4, -3, 0]; [-4, -2, -1]; [-3, -4, 2]; [-3, -3, 1]; [-3, -2, 0]; [-3, -1, -1];
[-2, -4, 3]; [-2, -1, 0]; [-2, -2, 1]; [-2, 2, -3]; [-1, -2, 2]; [-1, -3, 3]; [-1, -4, 4];
[-1, 0, 0]; [-1, -1, 1]; [0, -3, 4]; [0, -2, 3]; [0, -1, 2]; [0, 0, 1]; [1, -1, 3];
[1, -2, 4]; [1, 2, 0]; [2, -1, 4]; [2, 3, 0]; [2, 2, 1]; [3, 3, 1]; [3, 2, 2];
[3, 4, 0]; [4, 4, 1]; [4, 3, 2]

-2: [-4, -4, 2]; [-4, -3, 1]; [-4, -2, 0]; [-4, -1, -1]; [-3, -3, 2]; [-3, -2, 1]; [-3, -1, 0];
[-3, 3, -4]; [-2, -3, 3]; [-2, -4, 4]; [-2, 0, 0]; [-2, -1, 1]; [-2, -2, 2]; [-1, -2, 3];
[-1, -3, 4]; [-1, 1, 0]; [-1, -1, 2]; [0, -2, 4]; [0, 3, -1]; [0, 1, 1]; [0, 0, 2];
[1, -1, 4]; [1, 1, 2]; [1, 3, 0]; [2, 3, 1]; [2, 4, 0]; [3, 3, 2]; [3, 1, 4];
[4, 4, 2]; [4, 3, 3]

-3: [-4, -4, 3]; [-4, -3, 2]; [-4, -2, 1]; [-4, -1, 0]; [-3, -4, 4]; [-3, -3, 3]; [-3, -2, 2];
[-3, -1, 1]; [-3, 0, 0]; [-2, -3, 4]; [-2, -2, 3]; [-2, 1, 0]; [-2, 2, -1]; [-1, -2, 4];
[-1, 1, 1]; [-1, -1, 3]; [-1, 2, 0]; [0, -1, 4]; [0, 1, 2]; [0, 0, 3]; [1, 1, 3];
[1, 2, 2]; [1, 4, 0]; [2, 2, 3]; [2, 1, 4]; [3, 2, 4]; [4, 4, 3]

-4: [-4, -4, 4]; [-4, -3, 3]; [-4, -2, 2]; [-4, -1, 1]; [-4, 0, 0]; [-3, -3, 4]; [-3, 1, 0];
[-3, 2, -1]; [-3, 3, -2]; [-2, -2, 4]; [-2, 1, 1]; [-2, 2, 0]; [-2, 3, -1]; [-1, 1, 2];
[-1, -1, 4]; [-1, 3, 0]; [0, 0, 4]; [0, 2, 2]; [0, 3, 1]; [1, 1, 4]; [1, 2, 3];
[2, 2, 4]; [2, 3, 3]; [3, 3, 4]

-5: [-4, 1, 0]; [-4, 4, -3]; [-4, 3, -2]; [-4, 2, -1]; [-3, 1, 1]; [-3, 2, 0]; [-3, 3, -1];
[-3, 4, -2]; [-2, 2, 1]; [-2, 3, 0]; [-2, 4, -1]; [-1, 4, 0]; [-1, 3, 1]; [-1, 2, 2];
[0, 4, 1]; [0, 3, 2]; [1, 3, 3]; [1, 4, 2]; [2, 4, 3]; [3, 4, 4]

-6: [-4, 1, 1]; [-4, 4, -2]; [-4, 3, -1]; [-4, 2, 0]; [-3, 3, 0]; [-3, 2, 1]; [-3, 4, -1];
[-2, 2, 2]; [-2, 3, 1]; [-2, 4, 0]; [-1, 4, 1]; [-1, 3, 2]; [0, 4, 2]; [0, 3, 3];
[1, 4, 3]; [2, 4, 4]

-7: [-4, 4, -1]; [-4, 3, 0]; [-4, 2, 1]; [-3, 2, 2]; [-3, 3, 1]; [-3, 4, 0]; [-2, 2, 3];
[-2, 4, 1]; [-1, 3, 3]; [-1, 4, 2]; [0, 4, 3]; [1, 4, 4]

-8: [-4, 4, 0]; [-4, 3, 1]; [-4, 2, 2]; [-3, 1, 4]; [-3, 3, 2]; [-2, 2, 4]; [-2, 3, 3];
[-1, 3, 4]; [0, 4, 4]

-9: [-4, 4, 1]; [-4, 3, 2]; [-3, 3, 3]; [-3, 2, 4]; [-2, 3, 4]; [-1, 4, 4]
-10: [-4, 4, 2]; [-4, 3, 3]; [-3, 3, 4]; [-2, 4, 4]
-11: [-4, 4, 3]; [-3, 4, 4]
-12: [-4, 4, 4]

-11: [-3, -4, -4]
-10: [-3, -3, -4]; [-2, -4, -4]
-9: [-2, -3, -4]; [-1, -4, -4]
-8: [-2, -3, -3]; [-2, -2, -4]; [-1, -3, -4]; [0, -4, -4]
-7: [-2, -2, -3]; [-1, -2, -4]; [-1, -3, -3]; [0, -3, -4]; [1, -4, -4]
-6: [-1, -1, -4]; [-1, -2, -3]; [0, -3, -3]; [0, -2, -4]; [1, -3, -4]; [2, -4, -4]

-5: [-1, -2, -2]; [-1, -1, -3]; [0, -2, -3]; [0, -1, -4]; [1, -2, -4]; [1, -3, -3]; [2, -3, -4];
[3, -4, -4]

-4: [-1, -1, -2]; [0, -2, -2]; [0, -1, -3]; [0, 0, -4]; [1, -2, -3]; [1, -1, -4]; [2, -2, -4];
[2, -3, -3]; [3, -3, -4]; [4, -4, -4]

-3: [-3, -4, 4]; [0, -1, -2]; [0, 0, -3]; [0, 1, -4]; [1, -2, -2]; [1, -1, -3]; [2, -2, -3];
[2, -1, -4]; [3, -3, -3]; [3, -2, -4]

-2: [-2, -3, 3]; [-2, -4, 4]; [0, 0, -2]; [0, -1, -1]; [0, 1, -3]; [0, 2, -4]; [1, -1, -2];
[1, 1, -4]; [2, -2, -2]; [2, -1, -3]; [3, -1, -4]; [4, -3, -3]

-1: [-2, -3, 4]; [-1, -2, 2]; [-1, -3, 3]; [-1, -4, 4]; [0, 0, -1]; [0, 1, -2]; [0, 2, -3];
[0, 3, -4]; [1, -1, -1]; [1, 1, -3]; [1, 2, -4]; [3, -2, -2]

0: [-2, -2, 4]; [-1, -2, 3]; [-1, -3, 4]; [-1, -1, 2]; [0, 3, -3]; [0, 2, -2]; [0, 1, -1];
[0, 4, -4]; [1, 1, -2]; [1, 2, -3]; [1, 3, -4]; [2, 2, -4]

1: [-1, -2, 4]; [-1, 1, 1]; [0, 3, -2]; [0, 2, -1]; [0, 0, 1]; [0, 4, -3]; [1, 4, -4];
[1, 3, -3]; [1, 2, -2]; [2, 2, -3]; [2, 3, -4]; [3, -1, -1]

2: [-4, 3, 3]; [-3, 1, 4]; [-2, 2, 2]; [-2, 1, 3]; [-1, 1, 2]; [0, -1, 3]; [0, 1, 1];
[0, 4, -2]; [2, 0, 0]; [2, 3, -3]; [2, 4, -4]; [4, -1, -1]

3: [-3, 2, 4]; [-3, 3, 3]; [-2, 2, 3]; [-2, 1, 4]; [-1, 0, 4]; [-1, 1, 3]; [-1, 2, 2];
[0, 1, 2]; [3, 0, 0]; [3, 4, -4]

4: [-4, 4, 4]; [-3, 3, 4]; [-2, 2, 4]; [-2, 3, 3]; [-1, 1, 4]; [-1, 2, 3]; [0, 2, 2];
[0, 1, 3]; [0, 0, 4]; [1, 1, 2]

5: [-3, 4, 4]; [-2, 3, 4]; [-1, 2, 4]; [-1, 3, 3]; [0, 1, 4]; [0, 2, 3]; [1, 2, 2];
[1, 1, 3]

6: [-2, 4, 4]; [-1, 3, 4]; [0, 2, 4]; [0, 3, 3]; [1, 2, 3]; [1, 1, 4]
7: [-1, 4, 4]; [0, 3, 4]; [1, 2, 4]; [1, 3, 3]; [2, 2, 3]
8: [0, 4, 4]; [1, 3, 4]; [2, 2, 4]; [2, 3, 3]
9: [1, 4, 4]; [2, 3, 4]
10: [2, 4, 4]; [3, 3, 4]
11: [3, 4, 4]

Posted on: Sun Feb 09, 2020 12:43 am

Posts: 753
Joined: Fri May 13, 2011 1:37 am
Re: -4 to 4 puzzle combos
WOW.......How long did this take.......very impressive........am still curious as to how many puzzlers solve (on an average week) the -3 to +3 puzzle......I think it might be one of the lowest numbers of solvers.......this table of yours will certainly help those who have not been successful or not bother to try.

Posted on: Sun Feb 09, 2020 3:13 am

Posts: 81
Joined: Tue Apr 24, 2012 7:47 pm
Re: -4 to 4 puzzle combos
Thanks, beaker - I'm glad you liked my tables. They took me several weeks to do when all was said and done, and I completed this "project" in 4 steps before posting here. First, I had to write all of my number layouts down which took a considerable amount of time in itself. Next, I needed to crunch the numbers to see what each combo equaled. The third step was to make tables from all of that raw data and sort my combos out by cage value. My 3-cell subtraction table alone has 25 possibilities for the cage value (zero, +1 to +12 inclusive and -1 to -12 inclusive). The last thing I had to do before posting here was to refine my tables to get rid of any "copycat" combos. I'm sure everybody here has places they need to be, and the Department of Redundancy Department simply isn't one of them.

Among others, you can get a sum of +6 with the combo [1, 2, 3]. The order of the numbers does NOT matter for addition, so the 1, 2, and 3 could be entered in any way and still give +6 for the result. Now suppose that the same 1, 2, and 3 appeared in a 3-cell subtraction cage. What would that work out to? It depends on what number is being subtracted from what number, so the order DOES matter for subtraction. I've decided to do a little experiment below to prove my point.

1 - 2 - 3 = -4
2 - 1 - 3 = -2
3 - 2 - 1 = 0

Now let's make the above numbers negative and see what we get for the answers.

(-1) - (-2) - (-3) = 4
(-2) - (-1) - (-3) = 2
(-3) - (-2) - (-1) = 0

Now we see the variety of values that can arise from the order of subtraction cages. When working with the subtraction combos I've provided, take the leftmost digit followed by the middle digit and finally the rightmost digit in that exact order. So, for subtraction, the combo [2, 4, -1] really means

2 - 4 - (-1)

which equals -1. I have no idea what sort of negative numbers puzzles I or anybody here may have to deal with, but it's ultimately the thought that counts.

Posted on: Sun Feb 09, 2020 3:33 am

Posts: 753
Joined: Fri May 13, 2011 1:37 am
Re: -4 to 4 puzzle combos
Nice explanation with the negative number 3 cell cage as those are the most difficult......my way is to look at those cages and find the different combo's that work and then see which will agree best with the surrounding cages also with multiple possibilities......I find I "muddle" through a lot of combinations and watching where the "0"s might pop up and also doing the + cages (there are few of them) right away......still takes about 20 - 30 minutes to solve them (for me).......but, the next day, when I look back at how many solved the puzzle I find the number to be quite low in comparison to other more difficult puzzles.......maybe pnm could shed some light on whether this is the least completed of the regular weekly puzzles:)

Posted on: Sun Feb 09, 2020 4:20 am

Posts: 81
Joined: Tue Apr 24, 2012 7:47 pm
Re: -4 to 4 puzzle combos
It was my pleasure helping you out, beaker. I compiled these tables not only for myself, but for everybody here as well. I can't guarantee that any given solver will get a -4 to +4 puzzle, but I've got the bases covered if they do. The same is true if they get anything within that range (-1 to +3 for example).

skeeter84

Posted on: Wed Feb 12, 2020 8:34 am

Posts: 54
Joined: Fri May 13, 2011 2:21 am
Re: -4 to 4 puzzle combos
Awesome work Skeeter 84, Much appreciated. I normally muddle my way through the negative ones with no real idea on what combo goes where but like Beaker I find if you can work your way around the zero cells & go from there I can get it done with a bit of trial & error here & there to work outr combos.

Posted on: Wed Feb 12, 2020 10:40 am

Posts: 81
Joined: Tue Apr 24, 2012 7:47 pm
Re: -4 to 4 puzzle combos
Thanks for the compliment, ineedaname, and it was my pleasure posting these tables for everybody to use.

skeeter84

Posted on: Wed Feb 12, 2020 9:35 pm

Posts: 37
Joined: Fri May 13, 2011 1:16 am
Re: -4 to 4 puzzle combos
yes, very good work, skeeter84, thank you, it can be useful to win time because I arrived to solve thses puzzle but it takes me many many minutes

Posted on: Thu Feb 13, 2020 1:22 am

Posts: 81
Joined: Tue Apr 24, 2012 7:47 pm
Re: -4 to 4 puzzle combos
Thanks, fzpowerman - I'm glad to see that people like my tables!

skeeter84

Posted on: Mon Apr 06, 2020 10:40 pm

Posts: 37
Joined: Fri May 13, 2011 1:16 am
Re: -4 to 4 puzzle combos
Hi Skeeter84 (or anybody),
you would be able to present us the same table with the "mod" operator including numbers between -5 and +5 (that is to say -5, -4, -3, -2, -1, 0, 1, 2, 3, 4 and 5) ?
That would help me (and probaly not only me... ) because I have some doubts about a few combos to solve 3 or 4 books puzzle.
I hope it will be ok because we have a lot of free time because of containment and I believe it's the same in U.S or everywhere...