# NineFind - Which 9 Numbers Are Correct?

Text Version:

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


From the website NineFind.com, instructions are:

"Select the digits from 1 to 9 in the grid once each so that each row and column adds up to 9 or less."

Unlike Sudoku and most number puzzles, this puzzle has all of its squares filled in. Your goal is to find, and circle, the 9 correct numbers, while removing the incorrect numbers along the way. If a number is already circled, that must be the correct one for that particular number, and other boxes with that same number can be removed. Other numbers can be removed using logic, i.e. "This number can't exist here, otherwise it will force the row or column to add up to more than 9."

Remove numbers by crossing them out or placing an X over them. Only nine squares will remain; not every row and column needs to have a number in it, and some rows and columns will add up to less to 9.

You never have to guess. Logic will always be enough to solve.

First, the easy deductions:

Next,

note that all three 4s are in the same row or column as the top-right 9. So that 9 must be unused (shaded).

Now the 9s can be used the same way to rule out the 7 in row 2, column 3; the 7s can rule out the 8 in row 4, column 1; the 8s can rule out the 4 in row 1, column 4.

And now repeat:

The 4 now rules out the other 9 in its column; the 9s rule out the other 8 in their column, as well as the 3.

A new deduction can be done here:

Columns 2 and 5 must have an 8 and a 7 used there, in either order. Either way, nothing else can be used in those columns, since the rest of the numbers are too big.

Similarly, rows 4 and 5 must have the 9 and 4. So neither the 6 or 7 there can be used.

And now the rest falls by process of elimination:

The only 6 left must be used; then the 7 is chosen, then the 8, then the 3, then the 2, and finally the 9 and 4.

• Looks great! There are a few different ways to attack it, and this was nicely worded! – Jon Mar 30 at 17:43

The final grid:

Step by step solution (I’ll clean up if needed in the morning):

1:

Get rid of numbers in the 5 and 1 rows and columns that make the sum greater than 9 (the four should also be removed):

2:

The fours eradicate the 9 top right. The remaining nines can remove a 7 and the remaining 7s can remove an 8:

3:

6s eradicate the 8 in the middle. Remaining 8s eradicate a 4, and remaking fours eradicate the 9:

4:

As the remaking fours and nines are in two rows, one must be in one and the other in the other. All numbers in the 9 column can be removed. All numbers greater than 5 can be removed from the 9 and four rows:

5:

From there there is one 6 left, which gets rid of a 7 which leaves one left. That one seven removes an 8 leaving one 8 left too:

6:

Finally, the 8 eradicating a 3 causes a chain reaction to reach the final grid:

• I've downvoted because posting an extremely barebones answer that appears to be solely for "reserving a spot" is... generally considered bad for the health of the site, at the very least. – Deusovi Mar 30 at 1:58
• @Deusovi ik and I’m sorry, I shouldnt have donethis, I’m just up late at night and need to crop and edit a load of photos, I’ll try and edit it all in one big go and quickly – Beastly Gerbil Mar 30 at 2:00
• @Deusovi I've upvoted because the answer is correct. Also, the tactic of getting the answer in quickly is used by everyone, isn't illegal and is just the nature of the game. – Jens Mar 30 at 2:05
• @Jens It's not about "tactics" or "the game" -- this is about answer quality. We should not encourage answers that are intentionally subpar in order to be fast; upvotes are not just for answers that are correct but answers that are high-quality, and an answer that is only half-finished is decidedly not high-quality. [...] – Deusovi Mar 30 at 4:33