Easy Beginner Sudoku - Free Printable
Educational worksheet: Easy Beginner Sudoku. Download and print for classroom or home learning activities.
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Show Answer Key & Explanations
Step-by-step solution for: Easy Beginner Sudoku
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Show Answer Key & Explanations
Step-by-step solution for: Easy Beginner Sudoku
To solve this Sudoku puzzle, we need to fill in the empty squares so that every row, every column, and every 3x3 box contains the numbers 1 through 9 exactly once.
Here is the step-by-step logic to find the missing numbers:
Step 1: Look at Row 5 (the middle row)
The numbers currently in Row 5 are: `8, 5, 7, 1, 2, 4, _, 9, _`.
The missing numbers are 3 and 6.
* Look at the column for the first empty spot (Column 7). It already has a 6 in it (in Row 4). So, we cannot put a 6 there.
* Therefore, the first empty spot must be 3, and the last empty spot must be 6.
* Row 5 is now: `8, 5, 7, 1, 2, 4, 3, 9, 6`.
Step 2: Look at Column 9 (the far right column)
The numbers currently in Column 9 are: `9, 7, _, 4, 6, 2, _, 5, 8`.
The missing numbers are 1 and 3.
* Look at Row 3. It already has a 1 (in the first square). So, the empty spot in Row 3, Column 9 cannot be 1. It must be 3.
* This means the other empty spot in Row 7, Column 9 must be 1.
* Column 9 is now complete.
Step 3: Look at Row 3
The numbers currently in Row 3 are: `1, 7, 4, 2, _, 3, _, _, 3` (wait, we just filled the last one with 3? No, let's re-check Row 3).
Original Row 3: `1, 7, 4, 2, _, 3, _, _, _`.
We found the last number is 3? Let's re-verify Step 2.
Column 9 had: 9, 7, [blank], 4, 6, 2, [blank], 5, 8. Missing 1, 3.
Row 3 starts with `1`. So Row 3, Col 9 cannot be 1. It is 3. Correct.
Row 7, Col 9 is 1. Correct.
Now back to Row 3: `1, 7, 4, 2, _, 3, _, _, 3`. Wait, I can't have two 3s.
Let's look at Row 3 again carefully from the image: `1, 7, 4, 2, [blank], 3, [blank], [blank], [blank]`.
The blanks are at positions 5, 7, 8, 9.
Numbers present: 1, 2, 3, 4, 7.
Missing numbers for Row 3: 5, 6, 8, 9.
Let's look at the boxes.
Top-Middle Box (Rows 1-3, Cols 4-6): Contains `4,6,7`, `8,1,_`, `2,_,3`. Missing numbers in this box are 5 and 9.
The empty spots are Row 2, Col 6 and Row 3, Col 5.
* Row 2 already has a 9? No, Row 2 is `9, _, 3, 8, 1, _, 4, 2, 7`. Missing 5 and 6.
* In the Top-Middle box, the empty spot at Row 2, Col 6 must be either 5 or 9. But Row 2 needs 5 or 6. The common number is 5.
* So, Row 2, Col 6 is 5.
* This means the other empty spot in the Top-Middle box (Row 3, Col 5) is 9.
* Now Row 2 needs a 6. The only empty spot left in Row 2 is Col 2. So Row 2, Col 2 is 6.
* Row 2 is now: `9, 6, 3, 8, 1, 5, 4, 2, 7`.
Step 4: Continue with Row 3
Row 3 so far: `1, 7, 4, 2, 9, 3, _, _, 3`? No, Col 9 was determined to be 3.
Let's re-list Row 3 knowns: `1, 7, 4, 2, 9, 3, [blank], [blank], 3`.
Wait, if Col 9 is 3, then Row 3 has two 3s (one at Col 6, one at Col 9). That is impossible.
Let's re-read Column 9 from the image carefully.
Image Col 9: `9, 7, [blank], 4, [blank], 2, [blank], 5, 8`.
Ah, Row 5 Col 9 was blank in my initial scan?
Image Row 5: `8, 5, 7, 1, 2, 4, _, 9, _`.
In Step 1, I said Row 5 missing 3,6.
Col 9 has `9,7,_,4,_,2,_,5,8`.
Let's restart the logic more carefully.
Corrected Step-by-Step Solution:
1. Row 5: `8, 5, 7, 1, 2, 4, _, 9, _`. Missing 3, 6.
* Check Column 7 (where the first blank is). Column 7 has `3,4,_,8,_,1,2,_,_`. It contains a 3? Yes, Row 1 Col 7 is 3.
* Since Column 7 already has a 3, the blank in Row 5, Col 7 cannot be 3. It must be 6.
* Therefore, the last blank in Row 5, Col 9 is 3.
* Row 5 is: `8, 5, 7, 1, 2, 4, 6, 9, 3`.
2. Column 9: Now contains `9, 7, _, 4, 3, 2, _, 5, 8`.
* Missing numbers are 1 and 6.
* Check Row 3. Row 3 is `1, 7, 4, 2, _, 3, _, _, _`. It already has a 1.
* So, Row 3, Col 9 cannot be 1. It must be 6.
* Therefore, Row 7, Col 9 is 1.
* Column 9 is: `9, 7, 6, 4, 3, 2, 1, 5, 8`.
3. Row 3: `1, 7, 4, 2, _, 3, _, _, 6`.
* Missing numbers are 5, 8, 9.
* Look at the Top-Middle Box (Rows 1-3, Cols 4-6). The numbers inside are `4,6,7`, `8,1,5` (we found R2C6=5 below? Let's check), `2,_,3`.
* Let's find Row 2 first.
* Row 2: `9, _, 3, 8, 1, _, 4, 2, 7`. Missing 5, 6.
* Check Column 2. It has `_, _, 7, 3, 5, 9, _, 8, 1`. It has a 5? Yes, Row 5 Col 2 is 5.
* So Row 2, Col 2 cannot be 5. It must be 6.
* Therefore, Row 2, Col 6 is 5.
* Row 2 is: `9, 6, 3, 8, 1, 5, 4, 2, 7`.
4. Back to Row 3: `1, 7, 4, 2, _, 3, _, _, 6`.
* Missing 5, 8, 9.
* The blank at Col 5 is in the Top-Middle Box. The box now has `4,6,7`, `8,1,5`, `2,_,3`. The only missing number in this box is 9.
* So, Row 3, Col 5 is 9.
* Now Row 3 is `1, 7, 4, 2, 9, 3, _, _, 6`. Missing 5, 8.
* Check Column 7. It has `3, 4, _, 8, 6, 1, 2, _, _`. It has an 8? Yes, Row 4 Col 7 is 8.
* So Row 3, Col 7 cannot be 8. It must be 5.
* Therefore, Row 3, Col 8 is 8.
* Row 3 is: `1, 7, 4, 2, 9, 3, 5, 8, 6`.
5. Row 1: `5, _, _, 4, 6, 7, 3, _, 9`.
* Missing 1, 2, 8.
* Check Column 2. Current values: `_, 6, 7, 3, 5, 9, _, 8, 1`. Missing 2, 4.
* Wait, Col 2 has `6,7,3,5,9,8,1`. Present: 1,3,5,6,7,8,9. Missing 2, 4.
* Row 1 Col 2 is blank. Row 7 Col 2 is blank.
* Row 1 already has a 4 (Col 4). So Row 1, Col 2 cannot be 4. It must be 2.
* Therefore, Row 7, Col 2 is 4.
* Now Row 1 is `5, 2, _, 4, 6, 7, 3, _, 9`. Missing 1, 8.
* Check Column 3. Values: `_, 3, 4, 1, 7, 6, _, 2, 1`? No, Row 9 Col 2 is 1.
* Let's check Column 3 properly.
* Col 3: `_, 3, 4, 1, 7, 6, _, 2, _`.
* We know Row 7 Col 2 is 4. Row 7 is `_, 4, _, _, 8, 9, 2, 6, 1`.
* Let's solve Row 7 later.
* Back to Row 1. Missing 1, 8 at Col 3 and Col 8.
* Check Column 8. Values: `_, 2, 8, 5, 9, 7, 6, _, _`.
* Col 8 has 8? Yes, Row 3 Col 8 is 8.
* So Row 1, Col 8 cannot be 8. It must be 1.
* Therefore, Row 1, Col 3 is 8.
* Row 1 is: `5, 2, 8, 4, 6, 7, 3, 1, 9`.
6. Column 3: `8, 3, 4, 1, 7, 6, _, 2, _`.
* Missing 5, 9.
* Check Row 7. `_, 4, _, _, 8, 9, 2, 6, 1`.
* Check Row 9. `_, 1, _, _, _, _, 7, _, 8`.
* In Column 3, the blanks are Row 7 and Row 9.
* Row 7 already has a 9 (Col 6). So Row 7, Col 3 cannot be 9. It must be 5.
* Therefore, Row 9, Col 3 is 9.
* Column 3 is: `8, 3, 4, 1, 7, 6, 5, 2, 9`.
7. Row 7: `_, 4, 5, _, 8, 9, 2, 6, 1`.
* Missing 3, 7.
* Check Column 1. Values: `5, 9, 1, 2, 8, 4, _, 7, _`.
* Check Column 4. Values: `4, 8, 2, 9, 1, 3, _, 6, _`.
* Row 7 Col 1 is blank. Row 7 Col 4 is blank.
* Column 1 has a 7? Yes, Row 8 Col 1 is 7.
* So Row 7, Col 1 cannot be 7. It must be 3.
* Therefore, Row 7, Col 4 is 7.
* Row 7 is: `3, 4, 5, 7, 8, 9, 2, 6, 1`.
8. Column 1: `5, 9, 1, 2, 8, 4, 3, 7, _`.
* Missing 6.
* So Row 9, Col 1 is 6.
9. Row 9: `6, 1, 9, _, _, _, 7, _, 8`.
* Missing 2, 3, 4, 5.
* Blanks at Col 4, 5, 6, 8.
* Check Column 4: `4, 8, 2, 9, 1, 3, 7, 6, _`. Missing 5.
* So Row 9, Col 4 is 5.
* Check Column 5: `6, 1, 9, 7, 2, _, 8, 4, _`.
* Wait, Row 6 Col 5 is blank?
* Row 6: `4, 9, 6, 3, _, 8, 1, 7, 2`. Missing 5.
* So Row 6, Col 5 is 5.
* Now Column 5 is `6, 1, 9, 7, 2, 5, 8, 4, _`. Missing 3.
* So Row 9, Col 5 is 3.
* Check Column 6: `7, 5, 3, 6, 4, 8, 9, 1, _`.
* Row 8 Col 6 is 1? Let's check Row 8.
* Row 8: `7, 8, 2, 6, 4, 1, _, _, 5`.
* Col 6 values: `7, 5, 3, 6, 4, 8, 9, 1, _`. Missing 2.
* So Row 9, Col 6 is 2.
* Now Row 9 is `6, 1, 9, 5, 3, 2, 7, _, 8`. Missing 4.
* So Row 9, Col 8 is 4.
* Row 9 is: `6, 1, 9, 5, 3, 2, 7, 4, 8`.
10. Finish Row 8: `7, 8, 2, 6, 4, 1, _, _, 5`.
* Missing 3, 9.
* Check Column 7: `3, 4, 5, 8, 6, 1, 2, _, 7`. Missing 9.
* So Row 8, Col 7 is 9.
* Therefore, Row 8, Col 8 is 3.
* Row 8 is: `7, 8, 2, 6, 4, 1, 9, 3, 5`.
11. Finish Row 6: `4, 9, 6, 3, 5, 8, 1, 7, 2`. (Already completed in step 9).
Final Grid Verification:
Row 1: 5 2 8 | 4 6 7 | 3 1 9
Row 2: 9 6 3 | 8 1 5 | 4 2 7
Row 3: 1 7 4 | 2 9 3 | 5 8 6
---------------------------
Row 4: 2 3 1 | 9 7 6 | 8 5 4
Row 5: 8 5 7 | 1 2 4 | 6 9 3
Row 6: 4 9 6 | 3 5 8 | 1 7 2
---------------------------
Row 7: 3 4 5 | 7 8 9 | 2 6 1
Row 8: 7 8 2 | 6 4 1 | 9 3 5
Row 9: 6 1 9 | 5 3 2 | 7 4 8
All rows, columns, and boxes contain 1-9 uniquely.
Final Answer:
5 2 8 4 6 7 3 1 9
9 6 3 8 1 5 4 2 7
1 7 4 2 9 3 5 8 6
2 3 1 9 7 6 8 5 4
8 5 7 1 2 4 6 9 3
4 9 6 3 5 8 1 7 2
3 4 5 7 8 9 2 6 1
7 8 2 6 4 1 9 3 5
6 1 9 5 3 2 7 4 8
Here is the step-by-step logic to find the missing numbers:
Step 1: Look at Row 5 (the middle row)
The numbers currently in Row 5 are: `8, 5, 7, 1, 2, 4, _, 9, _`.
The missing numbers are 3 and 6.
* Look at the column for the first empty spot (Column 7). It already has a 6 in it (in Row 4). So, we cannot put a 6 there.
* Therefore, the first empty spot must be 3, and the last empty spot must be 6.
* Row 5 is now: `8, 5, 7, 1, 2, 4, 3, 9, 6`.
Step 2: Look at Column 9 (the far right column)
The numbers currently in Column 9 are: `9, 7, _, 4, 6, 2, _, 5, 8`.
The missing numbers are 1 and 3.
* Look at Row 3. It already has a 1 (in the first square). So, the empty spot in Row 3, Column 9 cannot be 1. It must be 3.
* This means the other empty spot in Row 7, Column 9 must be 1.
* Column 9 is now complete.
Step 3: Look at Row 3
The numbers currently in Row 3 are: `1, 7, 4, 2, _, 3, _, _, 3` (wait, we just filled the last one with 3? No, let's re-check Row 3).
Original Row 3: `1, 7, 4, 2, _, 3, _, _, _`.
We found the last number is 3? Let's re-verify Step 2.
Column 9 had: 9, 7, [blank], 4, 6, 2, [blank], 5, 8. Missing 1, 3.
Row 3 starts with `1`. So Row 3, Col 9 cannot be 1. It is 3. Correct.
Row 7, Col 9 is 1. Correct.
Now back to Row 3: `1, 7, 4, 2, _, 3, _, _, 3`. Wait, I can't have two 3s.
Let's look at Row 3 again carefully from the image: `1, 7, 4, 2, [blank], 3, [blank], [blank], [blank]`.
The blanks are at positions 5, 7, 8, 9.
Numbers present: 1, 2, 3, 4, 7.
Missing numbers for Row 3: 5, 6, 8, 9.
Let's look at the boxes.
Top-Middle Box (Rows 1-3, Cols 4-6): Contains `4,6,7`, `8,1,_`, `2,_,3`. Missing numbers in this box are 5 and 9.
The empty spots are Row 2, Col 6 and Row 3, Col 5.
* Row 2 already has a 9? No, Row 2 is `9, _, 3, 8, 1, _, 4, 2, 7`. Missing 5 and 6.
* In the Top-Middle box, the empty spot at Row 2, Col 6 must be either 5 or 9. But Row 2 needs 5 or 6. The common number is 5.
* So, Row 2, Col 6 is 5.
* This means the other empty spot in the Top-Middle box (Row 3, Col 5) is 9.
* Now Row 2 needs a 6. The only empty spot left in Row 2 is Col 2. So Row 2, Col 2 is 6.
* Row 2 is now: `9, 6, 3, 8, 1, 5, 4, 2, 7`.
Step 4: Continue with Row 3
Row 3 so far: `1, 7, 4, 2, 9, 3, _, _, 3`? No, Col 9 was determined to be 3.
Let's re-list Row 3 knowns: `1, 7, 4, 2, 9, 3, [blank], [blank], 3`.
Wait, if Col 9 is 3, then Row 3 has two 3s (one at Col 6, one at Col 9). That is impossible.
Let's re-read Column 9 from the image carefully.
Image Col 9: `9, 7, [blank], 4, [blank], 2, [blank], 5, 8`.
Ah, Row 5 Col 9 was blank in my initial scan?
Image Row 5: `8, 5, 7, 1, 2, 4, _, 9, _`.
In Step 1, I said Row 5 missing 3,6.
Col 9 has `9,7,_,4,_,2,_,5,8`.
Let's restart the logic more carefully.
Corrected Step-by-Step Solution:
1. Row 5: `8, 5, 7, 1, 2, 4, _, 9, _`. Missing 3, 6.
* Check Column 7 (where the first blank is). Column 7 has `3,4,_,8,_,1,2,_,_`. It contains a 3? Yes, Row 1 Col 7 is 3.
* Since Column 7 already has a 3, the blank in Row 5, Col 7 cannot be 3. It must be 6.
* Therefore, the last blank in Row 5, Col 9 is 3.
* Row 5 is: `8, 5, 7, 1, 2, 4, 6, 9, 3`.
2. Column 9: Now contains `9, 7, _, 4, 3, 2, _, 5, 8`.
* Missing numbers are 1 and 6.
* Check Row 3. Row 3 is `1, 7, 4, 2, _, 3, _, _, _`. It already has a 1.
* So, Row 3, Col 9 cannot be 1. It must be 6.
* Therefore, Row 7, Col 9 is 1.
* Column 9 is: `9, 7, 6, 4, 3, 2, 1, 5, 8`.
3. Row 3: `1, 7, 4, 2, _, 3, _, _, 6`.
* Missing numbers are 5, 8, 9.
* Look at the Top-Middle Box (Rows 1-3, Cols 4-6). The numbers inside are `4,6,7`, `8,1,5` (we found R2C6=5 below? Let's check), `2,_,3`.
* Let's find Row 2 first.
* Row 2: `9, _, 3, 8, 1, _, 4, 2, 7`. Missing 5, 6.
* Check Column 2. It has `_, _, 7, 3, 5, 9, _, 8, 1`. It has a 5? Yes, Row 5 Col 2 is 5.
* So Row 2, Col 2 cannot be 5. It must be 6.
* Therefore, Row 2, Col 6 is 5.
* Row 2 is: `9, 6, 3, 8, 1, 5, 4, 2, 7`.
4. Back to Row 3: `1, 7, 4, 2, _, 3, _, _, 6`.
* Missing 5, 8, 9.
* The blank at Col 5 is in the Top-Middle Box. The box now has `4,6,7`, `8,1,5`, `2,_,3`. The only missing number in this box is 9.
* So, Row 3, Col 5 is 9.
* Now Row 3 is `1, 7, 4, 2, 9, 3, _, _, 6`. Missing 5, 8.
* Check Column 7. It has `3, 4, _, 8, 6, 1, 2, _, _`. It has an 8? Yes, Row 4 Col 7 is 8.
* So Row 3, Col 7 cannot be 8. It must be 5.
* Therefore, Row 3, Col 8 is 8.
* Row 3 is: `1, 7, 4, 2, 9, 3, 5, 8, 6`.
5. Row 1: `5, _, _, 4, 6, 7, 3, _, 9`.
* Missing 1, 2, 8.
* Check Column 2. Current values: `_, 6, 7, 3, 5, 9, _, 8, 1`. Missing 2, 4.
* Wait, Col 2 has `6,7,3,5,9,8,1`. Present: 1,3,5,6,7,8,9. Missing 2, 4.
* Row 1 Col 2 is blank. Row 7 Col 2 is blank.
* Row 1 already has a 4 (Col 4). So Row 1, Col 2 cannot be 4. It must be 2.
* Therefore, Row 7, Col 2 is 4.
* Now Row 1 is `5, 2, _, 4, 6, 7, 3, _, 9`. Missing 1, 8.
* Check Column 3. Values: `_, 3, 4, 1, 7, 6, _, 2, 1`? No, Row 9 Col 2 is 1.
* Let's check Column 3 properly.
* Col 3: `_, 3, 4, 1, 7, 6, _, 2, _`.
* We know Row 7 Col 2 is 4. Row 7 is `_, 4, _, _, 8, 9, 2, 6, 1`.
* Let's solve Row 7 later.
* Back to Row 1. Missing 1, 8 at Col 3 and Col 8.
* Check Column 8. Values: `_, 2, 8, 5, 9, 7, 6, _, _`.
* Col 8 has 8? Yes, Row 3 Col 8 is 8.
* So Row 1, Col 8 cannot be 8. It must be 1.
* Therefore, Row 1, Col 3 is 8.
* Row 1 is: `5, 2, 8, 4, 6, 7, 3, 1, 9`.
6. Column 3: `8, 3, 4, 1, 7, 6, _, 2, _`.
* Missing 5, 9.
* Check Row 7. `_, 4, _, _, 8, 9, 2, 6, 1`.
* Check Row 9. `_, 1, _, _, _, _, 7, _, 8`.
* In Column 3, the blanks are Row 7 and Row 9.
* Row 7 already has a 9 (Col 6). So Row 7, Col 3 cannot be 9. It must be 5.
* Therefore, Row 9, Col 3 is 9.
* Column 3 is: `8, 3, 4, 1, 7, 6, 5, 2, 9`.
7. Row 7: `_, 4, 5, _, 8, 9, 2, 6, 1`.
* Missing 3, 7.
* Check Column 1. Values: `5, 9, 1, 2, 8, 4, _, 7, _`.
* Check Column 4. Values: `4, 8, 2, 9, 1, 3, _, 6, _`.
* Row 7 Col 1 is blank. Row 7 Col 4 is blank.
* Column 1 has a 7? Yes, Row 8 Col 1 is 7.
* So Row 7, Col 1 cannot be 7. It must be 3.
* Therefore, Row 7, Col 4 is 7.
* Row 7 is: `3, 4, 5, 7, 8, 9, 2, 6, 1`.
8. Column 1: `5, 9, 1, 2, 8, 4, 3, 7, _`.
* Missing 6.
* So Row 9, Col 1 is 6.
9. Row 9: `6, 1, 9, _, _, _, 7, _, 8`.
* Missing 2, 3, 4, 5.
* Blanks at Col 4, 5, 6, 8.
* Check Column 4: `4, 8, 2, 9, 1, 3, 7, 6, _`. Missing 5.
* So Row 9, Col 4 is 5.
* Check Column 5: `6, 1, 9, 7, 2, _, 8, 4, _`.
* Wait, Row 6 Col 5 is blank?
* Row 6: `4, 9, 6, 3, _, 8, 1, 7, 2`. Missing 5.
* So Row 6, Col 5 is 5.
* Now Column 5 is `6, 1, 9, 7, 2, 5, 8, 4, _`. Missing 3.
* So Row 9, Col 5 is 3.
* Check Column 6: `7, 5, 3, 6, 4, 8, 9, 1, _`.
* Row 8 Col 6 is 1? Let's check Row 8.
* Row 8: `7, 8, 2, 6, 4, 1, _, _, 5`.
* Col 6 values: `7, 5, 3, 6, 4, 8, 9, 1, _`. Missing 2.
* So Row 9, Col 6 is 2.
* Now Row 9 is `6, 1, 9, 5, 3, 2, 7, _, 8`. Missing 4.
* So Row 9, Col 8 is 4.
* Row 9 is: `6, 1, 9, 5, 3, 2, 7, 4, 8`.
10. Finish Row 8: `7, 8, 2, 6, 4, 1, _, _, 5`.
* Missing 3, 9.
* Check Column 7: `3, 4, 5, 8, 6, 1, 2, _, 7`. Missing 9.
* So Row 8, Col 7 is 9.
* Therefore, Row 8, Col 8 is 3.
* Row 8 is: `7, 8, 2, 6, 4, 1, 9, 3, 5`.
11. Finish Row 6: `4, 9, 6, 3, 5, 8, 1, 7, 2`. (Already completed in step 9).
Final Grid Verification:
Row 1: 5 2 8 | 4 6 7 | 3 1 9
Row 2: 9 6 3 | 8 1 5 | 4 2 7
Row 3: 1 7 4 | 2 9 3 | 5 8 6
---------------------------
Row 4: 2 3 1 | 9 7 6 | 8 5 4
Row 5: 8 5 7 | 1 2 4 | 6 9 3
Row 6: 4 9 6 | 3 5 8 | 1 7 2
---------------------------
Row 7: 3 4 5 | 7 8 9 | 2 6 1
Row 8: 7 8 2 | 6 4 1 | 9 3 5
Row 9: 6 1 9 | 5 3 2 | 7 4 8
All rows, columns, and boxes contain 1-9 uniquely.
Final Answer:
5 2 8 4 6 7 3 1 9
9 6 3 8 1 5 4 2 7
1 7 4 2 9 3 5 8 6
2 3 1 9 7 6 8 5 4
8 5 7 1 2 4 6 9 3
4 9 6 3 5 8 1 7 2
3 4 5 7 8 9 2 6 1
7 8 2 6 4 1 9 3 5
6 1 9 5 3 2 7 4 8
Parent Tip: Review the logic above to help your child master the concept of printable sudoku for beginners.
