zedoku

last remaining cell

level 1 - super easy

a number can only go in one cell because all other empty cells are blocked by the same number in their row or column.

the "reserved chairs" analogy

imagine a movie theater with 9 seats in a row. most seats have "reserved" signs on them - someone else already booked them. only one seat is free!

in sudoku, each 3×3 box, row, or column is like that theater row. when you are looking for a specific number (like number 8), some cells are "reserved" because an 8 already exists in that cell's row or column. when only one cell is left unreserved, that's where the 8 goes!

example 1: finding 8 in a box

look at the top-right 3×3 box (highlighted area). we need to place the number 8. two empty cells are marked with "×" because they are blocked - one by the 8 in row 2, and one by the 8 in column 7. only one cell remains for the 8!

5
3
4
6
7
1
9
2
6
7
2
1
9
5
×
3
4
9
1
8
3
4
2
×
8
5
8
5
9
7
2
3
4
1
6
4
2
6
8
5
1
9
7
3
7
3
1
9
6
4
5
2
8
3
9
7
4
8
6
2
5
1
2
8
5
3
1
9
7
4
6
1
4
3
2
7
8
6
8
9
blocked cells
answer: 8 goes here!

example 2: finding 5 in a row

now let's look at row 4. we need to place the number 5. the cells marked with "×" are blocked because column 5 and column 8 already have a 5 in them. only the last cell in the row can take the 5!

2
6
9
4
1
8
3
7
5
5
1
8
3
7
9
4
6
2
7
3
4
6
5
2
1
8
9
9
8
7
2
×
3
6
×
5
4
2
1
5
8
6
9
3
7
3
5
6
9
4
7
8
2
1
8
9
3
7
6
4
5
1
4
6
4
5
8
2
1
7
9
3
1
7
2
5
9
3
8
4
6
blocked by column 5 and 8
answer: 5 belongs here

example 3: step-by-step finding

let's find where 3 goes in the middle 3×3 box step by step.

step 1: identify empty cells

the middle box has 3 empty cells. we need to find which one can hold the number 3.

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

step 2: check first empty cell

row 4 already has a 3 in column 8. so the first empty cell is blocked!

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

step 3: check second empty cell

row 5 already has a 3 in column 1. so the second empty cell is also blocked!

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

step 4: last cell remaining!

only one cell is left, and row 6 doesn't have a 3 yet. the 3 must go here!

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

key takeaway

the last remaining cell technique is all about elimination. when you are trying to place a number, check each empty cell in the box, row, or column. if all but one cell are blocked by the same number appearing elsewhere in their row or column, you have found your answer!

💡

pro tip: this technique works for rows, columns, and 3×3 boxes. always check all three when hunting for a number!

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