Eliminate some numbers so that each of the three rows contains the numbers 1 through 9 each exactly once

Question

Beginner puzzle

This puzzle is intended to be suitable for people who are new to puzzle solving.

Clarification: Both experienced solvers and new solvers are welcome to post solutions to this puzzle.

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Below is a grid with three rows. Some additional numbers are underneath the grid. For each column, the number underneath the grid indicates how many numbers in that column should be scratched out. The goal is for each row in the finished grid to contain the numbers 1 through 9 each exactly once.

2 1 8 5 6 7 8 5 4 6 3 9 2 3 1  <- Grid row 1
1 4 5 2 3 2 6 5 4 8 8 1 6 7 9  <- Grid row 2
9 6 2 1 3 8 3 2 4 5 4 7 6 1 9  <- Grid row 3

2 2 0 1 1 1 1 2 2 1 1 0 1 2 1

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Attribution: PUZZLEBOMB.co.uk. Puzzles by @stecks & @apaultaylor.

Answer 1

So the starting combination is

2 1 8 5 6 7 8 5 4 6 3 9 2 3 1  <- Grid row 1
1 4 5 2 3 2 6 5 4 8 8 1 6 7 9  <- Grid row 2
9 6 2 1 3 8 3 2 4 5 4 7 6 1 9  <- Grid row 3

2 2 0 1 1 1 1 2 2 1 1 0 1 2 1

Let's start by looking at

the bottom row with only 0 and remove all of the same digits from each row(meaning that we remove all 8s from row 1, 5s from row 2 and 2s from row 3 for the 0 in the third column). And immediately adapt the bottom row with new values:

 2 1 8 5 6 7 . 5 4 6 3 9 2 3 1  <- Grid row 1
 . 4 5 2 3 2 6 . 4 8 8 1 6 7 9  <- Grid row 2
 9 6 2 1 3 8 3 . 4 5 4 7 6 1 9  <- Grid row 3

 1 2 . 1 1 1 0 0 2 1 1 . 1 2 1

Then we can repeat it:

 2 1 8 5 6 7 . 5 4 6 3 9 2 3 1  <- Grid row 1
 . 4 5 2 3 2 6 . 4 8 8 1 . 7 9  <- Grid row 2
 9 6 2 1 . 8 3 . 4 5 4 7 6 1 9  <- Grid row 3

 1 2 . 1 0 1 . 0 2 1 1 . 0 2 1

And again:

 . 1 8 . 6 7 . 5 4 . 3 9 2 3 1  <- Grid row 1
 . 4 5 2 3 2 6 . 4 8 8 1 . 7 9  <- Grid row 2
 9 . 2 1 . 8 3 . 4 5 4 7 6 1 9  <- Grid row 3

 0 1 . 0 . 1 . . 2 0 1 . . 2 1

And again:

 . . 8 . 6 7 . 5 4 . 3 9 2 3 1  <- Grid row 1
 . 4 5 2 3 . 6 . 4 8 8 1 . 7 9  <- Grid row 2
 9 . 2 1 . 8 3 . 4 5 4 7 6 . .  <- Grid row 3

 . 0 . . . 0 . . 2 0 1 . . 1 0

Once more:

 . . 8 . 6 7 . 5 4 . 3 9 2 3 1  <- Grid row 1
 . 4 5 2 3 . 6 . . 8 . 1 . 7 9  <- Grid row 2
 9 . 2 1 . 8 3 . 4 5 4 7 6 . .  <- Grid row 3

 . 0 . . . . . . 1 . 0 . . 1 .

Two more to go:

 . . 8 . 6 7 . 5 4 . 3 9 2 3 1  <- Grid row 1
 . 4 5 2 3 . 6 . . 8 . 1 . 7 9  <- Grid row 2
 9 . 2 1 . 8 3 . . 5 4 7 6 . .  <- Grid row 3

 . . . . . . . . 0 . . . . 1 .

And last one:

 . . 8 . 6 7 . 5 4 . 3 9 2 . 1  <- Grid row 1
 . 4 5 2 3 . 6 . . 8 . 1 . 7 9  <- Grid row 2
 9 . 2 1 . 8 3 . . 5 4 7 6 . .  <- Grid row 3

 . . . . . . . . . . . . . 0 .

So the final answer would be:

 . . 8 . 6 7 . 5 4 . 3 9 2 . 1  <- Grid row 1
 . 4 5 2 3 . 6 . . 8 . 1 . 7 9  <- Grid row 2
 9 . 2 1 . 8 3 . . 5 4 7 6 . .  <- Grid row 3

Answer 2

2 1 8 5 6 7 . 5 4 6 3 9 2 3 1  <- Grid row 1
. 4 5 2 3 2 6 . 4 8 8 1 6 7 9  <- Grid row 2
9 6 2 1 3 8 3 . 4 5 4 7 6 1 9  <- Grid row 3

2 2(0)1 1 1 1 2 2 1 1(0)1 2 1

2 1 8 . 6 7 . 5 4 6 3 9 2 3 1  <- Grid row 1
. 4 5 2 3 2 6 . 4 8 8 1 . 7 9  <- Grid row 2
9 6 2 1 . 8 3 . 4 5 4 7 6 1 9  <- Grid row 3

2 2 0 1 1 1(1 2)2 1 1 0 1 2 1

. 1 8 . 6 7 . 5 4 . 3 9 2 3 1  <- Grid row 1
. 4 5 2 3 . 6 . 4 8 8 1 . 7 9  <- Grid row 2
9 . 2 1 . 8 3 . 4 5 4 7 6 . 9  <- Grid row 3

2 2 0(1 1)1 1 2 2 1 1 0(1)2 1

. 1 8 . 6 7 . 5 4 . 3 9 2 3 1  <- Grid row 1
. 4 5 2 3 . 6 . 4 8 . 1 . 7 9  <- Grid row 2
9 . 2 1 . 8 3 . 4 5 4 7 6 . .  <- Grid row 3

2)2 0 1 1 1 1 2 2(1)1 0 1 2 1

. . 8 . 6 7 . 5 4 . 3 9 2 . 1  <- Grid row 1
. 4 5 2 3 . 6 . 4 8 . 1 . 7 9  <- Grid row 2
9 . 2 1 . 8 3 . . 5 4 7 6 . .  <- Grid row 3

2 2 0 1 1 1 1 2 2 1(1)0 1 2(1

. . 8 . 6 7 . 5 4 . 3 9 2 . 1  <- Grid row 1
. 4 5 2 3 . 6 . . 8 . 1 . 7 9  <- Grid row 2
9 . 2 1 . 8 3 . . 5 4 7 6 . .  <- Grid row 3

2 2 0 1 1 1 1 2 2 1 1 0 1 2 1

Answer 3

So first of all you analise the colunms with the number (0) below

2 1 8 5 6 7 8 5 4 6 3 9 2 3 1  <- Grid row 1
1 4 5 2 3 2 6 5 4 8 8 1 6 7 9  <- Grid row 2
9 6 2 1 3 8 3 2 4 5 4 7 6 1 9  <- Grid row 3

2 2 0 1 1 1 1 2 2 1 1 0 1 2 1
    ^
    |

With this information we know that de row 1 as a 8 in that position so we can delete the other element 8, the same for row 2, delete the other 5...row 3 delete the other 2.

Now the trick is that the puzzle solves itself like magic!

We already know the number 8 is in the right place so when deleted the other 8 we also know that that the corresponded column says to delete 1 number but we already delete number 8! so the other numbers 6,3 must be in the right place!

 2 1 8 5 6 7     5 4 6 3 9 2 3 1  <- Grid row 1
 1 4 5 2 3 2 (6) 5 4 8 8 1 6 7 9  <- Grid row 2
 9 6 2 1 3 8 (3) 2 4 5 4 7 6 1 9  <- Grid row 3

 2 2 0 1 1 1 1 2 2 1 1 0 1 2 1

This logic is applied for all the puzzle!

Print of the solution: [1]: https://i.sstatic.net/vTTasYNo.png