Question

fill the grid with the letters b, o, a, t once in each row, column and region.
(grid with some pre - filled letters: first row fourth cell a; second row second cell b, fourth cell t; third row first cell t, second cell o, third cell a, fourth cell b; fourth row first cell b, second cell a, third cell t, fourth cell o)
4 by 4 sudoku for kids

Explanation:

Step1: Analyze Row 3 (T, O, A, B) and Row 4 (B, A, T, O) to find patterns. Let's focus on Column 1 first. Column 1 has T (Row3), B (Row4). So missing letters: O, A. Row1 Column1: possible O or A. Row2 Column1: possible O or A (but Row2 has B in Column2, T in Column4).

Step2: Analyze Region (top-left 2x2). Row1 Column2, Row2 Column1 and 2. Row2 Column2 is B, so top-left region (Rows1-2, Columns1-2) needs O, A, B? Wait, letters are B, O, A, T? Wait, original letters: B, O, A, T? Wait, the problem says "Fill the grid with the letters B, O, A, once in each row, column and region" – wait, maybe typo, but grid has T. So letters are B, O, A, T. So each row, column, region (2x2) has B, O, A, T once.

Step3: Let's list rows:

Row 1: [?, ?, ?, A]
Row 2: [?, B, ?, T]
Row 3: [T, O, A, B]
Row 4: [B, A, T, O]
Columns:
Column 1: [?, ?, T, B] → needs O, A
Column 2: [?, B, O, A] → needs T,? Wait Row1 Col2, Row2 Col2 is B, Row3 Col2 O, Row4 Col2 A. So Column2: missing T (Row1 Col2) and? Wait no, 4 columns, each with B, O, A, T. Column2 has B (Row2), O (Row3), A (Row4) → missing T (Row1 Col2). So Row1 Col2 = T.

Step4: Row1: [?, T,?, A]. Now Row1 has T, A. Needs B, O. Column1: Row1 Col1 can be O or A? No, Column1 has T (Row3), B (Row4) → needs O, A. Row1 Col1: let's check region (top-left: Rows1-2, Cols1-2). Row1 Col2=T, Row2 Col2=B. So top-left region needs O, A. So Row1 Col1 and Row2 Col1 must be O and A.

Step5: Row2: [?, B,?, T]. Row2 has B, T. Needs O, A. Column1: Row2 Col1 is O or A. Let's check Column4: Row1 Col4=A, Row2 Col4=T, Row3 Col4=B, Row4 Col4=O → perfect, Column4 has A, T, B, O (all unique).

Step6: Column3: Row3 Col3=A, Row4 Col3=T. So Column3 needs B, O. Row1 Col3: let's see Row1: [C1, T, C3, A]. Needs B, O. So C1 and C3 are B and O. Let's check Region top-right (Rows1-2, Cols3-4). Row1 Col4=A, Row2 Col4=T. So top-right region needs B, O. So Row1 Col3 and Row2 Col3 must be B and O.

Step7: Let's do Row3 and Row4 first (already filled: Row3: T, O, A, B; Row4: B, A, T, O). Now Row2: [C1, B, C3, T]. C1: O or A (Column1 needs O, A). C3: B or O (Column3 needs B, O). Let's check Row2: needs O and A (since has B, T). So if C1 is A, then C3 is O (because Row2 needs O and A: C1=A, C3=O). Let's test:

Row2: [A, B, O, T]. Now check Column1: Row2 Col1=A, so Row1 Col1=O (since Column1 needs O, A: Row1 Col1=O, Row2 Col1=A).

Step8: Row1: [O, T,?, A]. Now Row1 needs B (since has O, T, A). So Row1 Col3=B. Check Column3: Row1 Col3=B, Row2 Col3=O, Row3 Col3=A, Row4 Col3=T → perfect (B, O, A, T).

Step9: Now fill:

Row1: O, T, B, A
Row2: A, B, O, T
Row3: T, O, A, B
Row4: B, A, T, O
Check regions (2x2):
Top-left (R1-2, C1-2): O, T; A, B → O, T, A, B (all unique)
Top-right (R1-2, C3-4): B, A; O, T → B, A, O, T (all unique)
Bottom-left (R3-4, C1-2): T, O; B, A → T, O, B, A (all unique)
Bottom-right (R3-4, C3-4): A, B; T, O → A, B, T, O (all unique)
Columns:
Column1: O, A, T, B → O, A, T, B (unique)
Column2: T, B, O, A → T, B, O, A (unique)
Column3: B, O, A, T → B, O, A, T (unique)
Column4: A, T, B, O → A, T, B, O (unique)
Rows:
Row1: O, T, B, A → O, T, B, A (unique)
Row2: A, B, O, T → A, B, O, T (unique)
Row3: T, O, A, B → T, O, A, B (unique)
Row4: B, A, T, O → B, A, T, O (unique)

So the filled grid is:

Row 1: O, T, B, A

Row 2: A, B, O, T

Row 3: T, O, A, B

Row 4: B, A, T, O

Answer:

The filled grid (row-wise) is:
Row 1: O, T, B, A
Row 2: A, B, O, T
Row 3: T, O, A, B
Row 4: B, A, T, O

(If you need the grid in table form:

	Col1	Col2	Col3	Col4
Row2	A	B	O	T
Row3	T	O	A	B
Row4	B	A	T	O	)