## 40 Sum - When Sudoku and Kakuro meets

Notes on possible new logic puzzles

### 40 Sum - When Sudoku and Kakuro meets

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 #18 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 #21 - - - 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 #37 - 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 #48 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: 16
Joined: 16 November 2015

### Re: 40 Sum - When Sudoku and Kakuro meets

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: 16
Joined: 16 November 2015

### Re: 40 Sum - When Sudoku and Kakuro meets

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: 16
Joined: 16 November 2015

### Re: 40 Sum - When Sudoku and Kakuro meets

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: 16
Joined: 16 November 2015

### Re: 40 Sum - When Sudoku and Kakuro meets

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
Serg
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Posts: 727
Joined: 01 June 2010
Location: Russia

### Re: 40 Sum - When Sudoku and Kakuro meets

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: 16
Joined: 16 November 2015

### Re: 40 Sum - When Sudoku and Kakuro meets

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
Serg
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Posts: 727
Joined: 01 June 2010
Location: Russia

### Re: 40 Sum - When Sudoku and Kakuro meets

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 - 95 - - 8 - - 6- 3 7 - - 2 -- 8 - - - 5 74 - - 7 - 9 -`
bhimz

Posts: 16
Joined: 16 November 2015

### Re: 40 Sum - When Sudoku and Kakuro meets

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 - 95 - - 8 - - 6- 3 7 - - 2 -- 8 - - - 5 74 - - 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
Serg
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Posts: 727
Joined: 01 June 2010
Location: Russia

### Re: 40 Sum - When Sudoku and Kakuro meets

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: 16
Joined: 16 November 2015

### Re: 40 Sum - When Sudoku and Kakuro meets

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 59 8 5 6 7 2 37 6 1 4 8 5 98 5 7 9 6 3 24 9 6 1 5 8 75 1 8 7 4 9 66 4 9 5 1 7 8`

The puzzle has unique solution.

Serg
Serg
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Posts: 727
Joined: 01 June 2010
Location: Russia

### Re: 40 Sum - When Sudoku and Kakuro meets

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

Here's puzzle #16:

Code: Select all
`9 - - 5 - - 61 - 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: 16
Joined: 16 November 2015

### Re: 40 Sum - When Sudoku and Kakuro meets

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

Code: Select all
`9 - - 5 - - 61 - 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 61 4 6 8 9 7 58 9 5 7 6 3 27 6 4 1 8 5 95 8 9 6 7 2 36 1 7 4 5 9 84 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).

Serg
Serg
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Posts: 727
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Location: Russia

### Re: 40 Sum - When Sudoku and Kakuro meets

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.
HATMAN

Posts: 272
Joined: 25 February 2006
Location: Nigeria

### Re: 40 Sum - When Sudoku and Kakuro meets

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

m_b_metcalf
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