40 Sum - When Sudoku and Kakuro meets

Notes on possible new logic puzzles

40 Sum - When Sudoku and Kakuro meets

Postby bhimz » Wed Jan 06, 2016 12:57 am

Hi, this is my first puzzle submission for the forum so all comments and critics are very welcomed :)

The idea for this puzzle came from when I was trying to create a new form of Sudoku. As I was playing around with the numbers, I found out that the largest 5 number combination is 5+6+7+8+9 = 35 (obviously) and that the remaining number (1,2,3,4) can be used to form a 5. Based on this, I created a 7x7 grid Sudoku/Kakuro inspired puzzle game. Hence, 40 Sum was born.

The rules are pretty simple actually, especially if you're familiar with both games:
- The objective of the game is to fill a 7x7 grid with numbers between 1-9 (Since there are only 7 columns and 7 rows, you can skip 2 numbers on each)
- Similar to Sudoku, each number must NOT be repeated in the same column, the same row, or any 1 cell around it.
- The sum of all the numbers in each row/column must be equal to 40.

Here is a sample of a completed puzzle:
Before:
5 - - 1 - - -
- 2 - 9 6 8 7
9 6 8 7 2 5 3
8 - 3 - - - -
6 9 2 - - - -
2 - - - 5 9 8
7 5 9 - 8 1 -

Solved:
5 8 6 1 7 4 9 - 40
3 2 5 9 6 8 7 - 40
9 6 8 7 2 5 3 - 40
8 7 3 5 9 6 2 - 40
6 9 2 8 3 7 5 - 40
2 3 7 6 5 9 8 - 40
7 5 9 4 8 1 6- 40
| | | | | | |
40404040404040

For you wondering on how to solve the puzzle, here are the steps (don't open it if you want to figure it out yourself):

Hidden Text: Show
- First, try to find column/row with only 1 empty cell. If there is one, try working your way from there.
- Like I said before, the largest combination possible is 5+6+7+8+9 = 35, which means that each row/column WILL have these five numbers. These are called the base numbers. Try placing them first. You can use elimination like a normal sudoku (like looking at all the positions of 5 in all row/column)
- Since the sum of all base numbers are 35, you only need 5 more to make it 40. This can be 1+4 = 5, or 2+3 = 5. These pairs are called the supplementary or key numbers. Look out for hints of which pair is in the column/row. For instance, if you see a 4 in a row, then you can guess that there's 1 somewhere in that same row. Likewise, you can also check the columns to pinpoint the location of the pair, or to eliminate columns (for instance, you're looking for 1 in the row like our previous example, then you check the column and see a 3, therefor that column must not contain a 1 and can be eliminated)


Sorry is my English is not so good btw, it's not my primary language.

Here's a couple more of the puzzles to try out, see I you can figure out the answer! I'll be posting the solution next week.

Code: Select all
Puzzle #1

8 7 1 5 9 - -
- - - 7 8 1 -
7 - 5 - - 9 4
- 3 6 - 7 - 8
9 5 8 4 1 6 -
3 - - - - 8 -
- 6 - 8 - 7 1



Code: Select all
Puzzle #2

1 - - - 9 - -
5 7 9 - 1 6 8
- 3 8 5 - - -
9 - 7 - 8 - 3
- - - 1 - 7 9
- 9 4 8 - 1 -
4 5 - - - 8 -



Code: Select all
Puzzle #3

7 - 4 6 5 - -
1 5 - 7 8 6 -
8 4 6 - - - 7
6 - - - 4 8 5
- - 5 8 6 7 1
5 - 7 - - 4 8
- - 8 4 7 5 6



Code: Select all
Puzzle #4

8 9 5 4 - - 7
6 1 7 8 5 - -
9 5 4 6 - - -
7 6 - - - 4 -
- - - - 6 8 1
- 8 6 - 4 - -
4 7 - 9 8 5 6



Code: Select all
Puzzle #5

- - - 4 - - -
- - - - 7 4 -
5 - 7 9 - 8 1
1 - 6 - - 7 -
7 8 - - 4 9 -
- 1 - 6 8 5 -
6 5 4 - - - -
bhimz
 
Posts: 14
Joined: 16 November 2015

Re: 40 Sum - When Sudoku and Kakuro meets

Postby bhimz » Mon Jan 11, 2016 1:26 am

Decided to post new puzzles every two days, and then the solutions. First, here are the solutions for the previous five:

Puzzle #1:
Hidden Text: Show
8 7 1 5 9 4 6
6 9 4 7 8 1 5
7 8 5 1 6 9 4
2 3 6 9 7 5 8
9 5 8 4 1 6 7
3 2 7 6 5 8 9
5 6 9 8 4 7 1


Puzzle #2:
Hidden Text: Show
1 8 6 7 9 4 5
5 7 9 4 1 6 8
6 3 8 5 7 9 2
9 2 7 6 8 5 3
8 6 5 1 4 7 9
7 9 4 8 5 1 6
4 5 1 9 6 8 7


Puzzle #3:
Hidden Text: Show
7 8 4 6 5 1 9
1 5 9 7 8 6 4
8 4 6 5 1 9 7
6 7 1 9 4 8 5
4 9 5 8 6 7 1
5 6 7 1 9 4 8
9 1 8 4 7 5 6


Puzzle #4:
Hidden Text: Show
8 9 5 4 1 6 7
6 1 7 8 5 9 4
9 5 4 6 7 1 8
7 6 8 1 9 4 5
5 4 9 7 6 8 1
1 8 6 5 4 7 9
4 7 1 9 8 5 6


Puzzle #5:
Hidden Text: Show
9 7 8 4 1 6 5
8 6 1 5 7 4 9
5 4 7 9 6 8 1
1 9 6 8 5 7 4
7 8 5 1 4 9 6
4 1 9 6 8 5 7
6 5 4 7 9 1 8


Did you get it right? What do you think? Is it interesting? Was it too easy or too hard? Please share some feedback! Anyway, here are the next ones: decided to make one of them harder, please try them out and let me know what you think, or you can also post your solutions here ;)

Puzzle #6:
Code: Select all
- 5 9 7 8 1 -
8 2 - - 9 5 7
- - - 2 6 - -
2 9 - 8 5 - 6
- - - 6 - - 1
9 - 2 - - 6 -
7 - 8 9 1 - 5


Puzzle #7:
Code: Select all
4 6 - - 7 - 8
- 8 - 2 - - -
- - - 9 5 8 3
- 9 - 8 - - 2
8 3 - 7 2 5 -
- 5 2 - 8 - -
- 7 8 6 9 4 -
bhimz
 
Posts: 14
Joined: 16 November 2015

Re: 40 Sum - When Sudoku and Kakuro meets

Postby bhimz » Wed Jan 13, 2016 12:35 am

Here are the solutions for the previous puzzles:

Puzzle #6:
Hidden Text: Show
6 5 9 7 8 1 4
8 2 6 3 9 5 7
3 7 5 2 6 8 9
2 9 3 8 5 7 6
5 8 7 6 4 9 1
9 3 2 5 7 6 8
7 6 8 9 1 4 5


Puzzle #7:
Hidden Text: Show
4 6 9 5 7 1 8
5 8 3 2 6 9 7
6 2 7 9 5 8 3
7 9 5 8 3 6 2
8 3 6 7 2 5 9
9 5 2 3 8 7 6
1 7 8 6 9 4 5


And here are a couple of new ones:

Puzzle #8:
Code: Select all
9 4 - - - - 5
6 7 8 - - 2 -
- 5 2 7 - - 9
2 8 9 6 - 5 -
7 - - - 2 9 -
5 - - - - - 2
8 - 5 4 9 - -


Puzzle #9:
Code: Select all
1 5 4 8 7 - -
6 7 9 - 4 5 -
9 - - - - 7 4
- 8 7 4 - - 6
- 4 - 9 - 8 -
- - - - - 4 -
- - - - 9 1 7


Have fun!
bhimz
 
Posts: 14
Joined: 16 November 2015

Re: 40 Sum - When Sudoku and Kakuro meets

Postby bhimz » Thu Jan 21, 2016 1:16 am

Missed posting a couple of days due to some work, so I decide to post 4 puzzles this time.

First off, the solutions for the previous ones:

Puzzle #8:
Hidden Text: Show
9 4 6 1 7 8 5
6 7 8 9 5 2 3
3 5 2 7 8 6 9
2 8 9 6 3 5 7
7 6 3 5 2 9 8
5 9 7 8 6 3 2
8 1 5 4 9 7 6


Puzzle #9:
Hidden Text: Show
1 5 4 8 7 6 9
6 7 9 1 4 5 8
9 1 5 6 8 7 4
5 8 7 4 1 9 6
7 4 6 9 5 8 1
8 9 1 7 6 4 5
4 6 8 5 9 1 7


Code: Select all
Puzzle #10:

3 8 5 - 7 6 -
- - 6 8 3 - 5
6 5 2 7 9 - -
8 - - 3 - - 6
- 3 8 - 6 9 7
- - - 9 - 3 2
9 - 3 - - - 8

Puzzle #11:

- 7 - - 6 2 -
9 - - 2 - - -
8 - 7 - - 6 2
2 6 - - - 7 9
5 8 2 7 9 - 6
- 9 - 6 2 - -
- 2 - 5 - 9 7

Puzzle #12:

3 8 - 9 - - 5
7 9 - 5 8 3 6
- 3 - - 2 9 -
- 6 - - - - 2
2 7 9 - 5 - -
8 - 6 2 - 7 9
6 - 3 - 9 - -

Puzzle #13:

3 8 - 9 - - 5
7 9 - 5 8 3 6
- 3 - - 2 9 -
- 6 - - - - 2
2 7 9 - 5 - -
8 - 6 2 - 7 9
6 - 3 - 9 - -


Meanwhile, I could really use for some feedback guys... Tell me what you think of the puzzles; is it good, just okay or too simple? Any feedback is good enough, please shoot me some.
bhimz
 
Posts: 14
Joined: 16 November 2015

Re: 40 Sum - When Sudoku and Kakuro meets

Postby Serg » Fri Jan 22, 2016 5:18 pm

Hi, bhimz!
I tried to solve your Puzzle #10.
bhimz wrote:
Code: Select all
Puzzle #10:

3 8 5 - 7 6 -
- - 6 8 3 - 5
6 5 2 7 9 - -
8 - - 3 - - 6
- 3 8 - 6 9 7
- - - 9 - 3 2
9 - 3 - - - 8


Meanwhile, I could really use for some feedback guys... Tell me what you think of the puzzles; is it good, just okay or too simple? Any feedback is good enough, please shoot me some.

This puzzle is too simple. It can be solved by "singles" only, even "naked pairs" or "hidden pairs" techniques are not necessary. I had a look to other puzzles. They all are similar. You should decrease number of givens. What can one say about sudoku puzzles having 7 givens in a row/column?

Serg
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Re: 40 Sum - When Sudoku and Kakuro meets

Postby bhimz » Mon Jan 25, 2016 12:58 am

Hi serg,
Thank you so much for the feedback! Seems I still need more knowledge on sudoku puzzle solving/building one; I'll see what I can do for the next ones. Btw, by givens do you mean hints? I'm not very familiar with the terms.
bhimz
 
Posts: 14
Joined: 16 November 2015

Re: 40 Sum - When Sudoku and Kakuro meets

Postby Serg » Mon Jan 25, 2016 1:22 pm

Hi, bhimz!
bhimz wrote:Hi serg,
Btw, by givens do you mean hints? I'm not very familiar with the terms.

Yes, "givens" or "clues" are a priori known digits according to sudoku terminology. I think, "40 Sum" puzzle should have not more than 2-3 givens per row.

Serg
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Re: 40 Sum - When Sudoku and Kakuro meets

Postby bhimz » Tue Jan 26, 2016 4:58 am

Thanks again for the insight!
Based on your feedback, I made some modifications and made 2 new puzzles; I would be delighted if you can take a look and give me some comments about them:

Code: Select all
Puzzle #14:
1 - 4 - - 6 -
9 - 5 - - 2 3
- 6 - 4 - - 9
- - - 9 6 - -
4 - - - 5 - 7
- 1 8 - 4 - -
- 4 - 5 - 7 -

Puzzle #15:
8 - 3 - 9 - -
- - 8 - 5 - -
- - - - 2 - 9
5 - - 8 - - 6
- 3 7 - - 2 -
- 8 - - - 5 7
4 - - 7 - 9 -
bhimz
 
Posts: 14
Joined: 16 November 2015

Re: 40 Sum - When Sudoku and Kakuro meets

Postby Serg » Tue Jan 26, 2016 8:27 pm

Hi, bhimz!
bhimz wrote:I made some modifications and made 2 new puzzles; I would be delighted if you can take a look and give me some comments about them:

Code: Select all
Puzzle #14:
1 - 4 - - 6 -
9 - 5 - - 2 3
- 6 - 4 - - 9
- - - 9 6 - -
4 - - - 5 - 7
- 1 8 - 4 - -
- 4 - 5 - 7 -

Puzzle #15:
8 - 3 - 9 - -
- - 8 - 5 - -
- - - - 2 - 9
5 - - 8 - - 6
- 3 7 - - 2 -
- 8 - - - 5 7
4 - - 7 - 9 -

I solved Puzzle #14. It is a little bit harder than previous puzzles - it requires "naked pairs" technique. But it is still too easy. The next problem is great similarity between "40 Sum" and Sudoku - many Sudoku solving techniques are applicable to "40 Sum" solving. Instead I cannot see any nontrivial technique new to "40 Sum". Maybe you should further decrease number of givens to produce sufficiently hard puzzles.

Serg
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Re: 40 Sum - When Sudoku and Kakuro meets

Postby bhimz » Wed Jan 27, 2016 4:34 am

Awesome, glad that the puzzles have improved although a bit; I will try to tweak it down even further to see how it goes. Can you also submit your answers for puzzle #14 and #15, just to check if it's different from mine? Thanks again!
bhimz
 
Posts: 14
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Re: 40 Sum - When Sudoku and Kakuro meets

Postby Serg » Wed Jan 27, 2016 7:44 pm

Hi, bhimz
bhimz wrote:Can you also submit your answers for puzzle #14 and #15, just to check if it's different from mine? Thanks again!

This is solution of Puzzle #14 (I solved #14 only):
Code: Select all
1 7 4 8 9 6 5
9 8 5 6 7 2 3
7 6 1 4 8 5 9
8 5 7 9 6 3 2
4 9 6 1 5 8 7
5 1 8 7 4 9 6
6 4 9 5 1 7 8

The puzzle has unique solution.

Serg
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Re: 40 Sum - When Sudoku and Kakuro meets

Postby bhimz » Fri Jan 29, 2016 12:11 pm

Great! It's indeed identical with my answer.. Also, here's the solution for #15, if anyone else is looking for it:

Hidden Text: Show
Puzzle #15

8 7 3 2 9 6 5
1 9 8 6 5 7 4
7 6 5 3 2 8 9
5 2 9 8 7 3 6
9 3 7 5 6 2 8
6 8 2 9 3 5 7
4 5 6 7 8 9 1


I've tweaked a bit more, and come up with this next one.. So far, it's the hardest I can get with the current rule set; reducing givens any further seems to make the puzzle too hard/complicated to solve ..or maybe I still lack sudoku knowledge to make it any harder :D

Here's puzzle #16:

Code: Select all
9 - - 5 - - 6
1 - 6 - - 7 -
- 9 - - 6 - -
- 6 - - - 5 -
5 - - 6 - - 3
- - 7 - 5 - 8
- 5 - 9 - - -


Please give a try and let me what you think of it
bhimz
 
Posts: 14
Joined: 16 November 2015

Re: 40 Sum - When Sudoku and Kakuro meets

Postby Serg » Fri Jan 29, 2016 5:42 pm

Hi, bhimz!
bhimz wrote:Here's puzzle #16:

Code: Select all
9 - - 5 - - 6
1 - 6 - - 7 -
- 9 - - 6 - -
- 6 - - - 5 -
5 - - 6 - - 3
- - 7 - 5 - 8
- 5 - 9 - - -


Please give a try and let me what you think of it

Here's solution of puzzle #16:
Code: Select all
9 7 1 5 4 8 6
1 4 6 8 9 7 5
8 9 5 7 6 3 2
7 6 4 1 8 5 9
5 8 9 6 7 2 3
6 1 7 4 5 9 8
4 5 8 9 1 6 7

It is more interesting, than previous, but is still too simple. The most complicated sudoku techniques used - "naked pairs" and "hidden pairs". At last I observed (simple) solving technique being unique to "40 Sum" puzzle (i.e. that technique isn't applicable to sudoku solving).

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Re: 40 Sum - When Sudoku and Kakuro meets

Postby HATMAN » Sat Aug 13, 2016 9:44 pm

40 by 40 V1A

Removed as not anti-king - I will re-post further down later.
Last edited by HATMAN on Tue Aug 16, 2016 5:37 pm, edited 1 time in total.
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Re: 40 Sum - When Sudoku and Kakuro meets

Postby m_b_metcalf » Mon Aug 15, 2016 10:00 am

Dear HATMAN,
Could I please ask you to check that this puzzle has a valid solution? Having failed to solve it by hand (having also discovered the 14/23 rule), I wrote a short program that also fails to find a complete solution (but that solves #16 correctly).

Thanks,

Mike Metcalf
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