Number Grid Puzzles worksheet for students to complete by filling in missing numbers in various grid patterns.

To solve these Number Grid Puzzles, we need to understand how a standard 100-chart (numbers 1 to 100) works.

The Rules of the Grid:
* Moving Right (+1): The number increases by 1.
* Moving Left (-1): The number decreases by 1.
* Moving Down (+10): The number increases by 10.
* Moving Up (-10): The number decreases by 10.

Let's solve each puzzle step-by-step using these rules.

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Puzzle 1
* Given: 16 is in the center.
* Above 16: $16 - 10 = \mathbf{6}$ (This matches the given 6).
* Below 16: $16 + 10 = \mathbf{26}$.
* Left of 25: Wait, let's look at the shape.
* Top row: Empty, 6, Empty.
* Middle row: Empty, 16, Empty.
* Bottom row: 25, Empty, Empty.
* Very bottom: Empty under the middle column? No, looking closely at Puzzle 1:
* Row 1: [ ] [6] [ ]
* Row 2: [ ] [16] [ ]
* Row 3: [25] [ ] [ ]
* Row 4: [ ] under the 25? Or under the 16? The box is under the 25. Let's re-examine the connections.
* Actually, usually these are connected blocks. Let's trace from known numbers.
* We have 6 and 16. $16 - 10 = 6$. So 6 is directly above 16. Correct.
* We have 25. Where is it relative to 16? It is in the next row down, but one column to the left.
* Let's find the number below 16: $16 + 10 = 26$.
* The number to the left of 26 is $26 - 1 = 25$. This matches the given 25. So the grid alignment is confirmed.
* Now fill in the blanks:
* Left of 6: $6 - 1 = \mathbf{5}$.
* Right of 6: $6 + 1 = \mathbf{7}$.
* Left of 16: $16 - 1 = \mathbf{15}$.
* Right of 16: $16 + 1 = \mathbf{17}$.
* Below 25: $25 + 10 = \mathbf{35}$.
* Below 26 (which is empty in the diagram but logically there): The box is under the 25. So just 35.
* Wait, let's look at the shape again.
* Col 1: Row 3 is 25. Row 4 is empty box.
* Col 2: Row 1 is 6. Row 2 is 16. Row 3 is empty. Row 4 is empty? No, the bottom box is under the 25.
* Let's assume the standard cross/shape logic.
* Box left of 6: 5
* Box right of 6: 7
* Box left of 16: 15
* Box right of 16: 17
* Box below 25: 35
* Is there a box below 16? The diagram shows a box under the 25. It does NOT show a box under the 16/26 position.
* So for Puzzle 1, the missing numbers are:
* Top-left: 5
* Top-right: 7
* Middle-left: 15
* Middle-right: 17
* Bottom-left (under 25): 35

Puzzle 2
* Given: 2 and 21.
* Shape:
* Row 1: [ ] [2]
* Row 2: [ ] [ ] [ ] (The 2 is above the middle box of this row?)
* Let's check alignment. If 2 is at position (row 1, col 2), then below it is (row 2, col 2).
* Value below 2: $2 + 10 = 12$.
* We have 21 in Row 3.
* Let's see where 21 is. It looks like it's in the first column of Row 3.
* If Row 2 Col 1 is $x$, then Row 3 Col 1 is $x+10$.
* Let's work backwards from 21.
* Above 21: $21 - 10 = 11$. So Row 2 Col 1 is 11.
* Right of 11: $11 + 1 = 12$. This matches the spot below 2 ($2+10=12$). So the alignment is correct.
* Right of 12: $12 + 1 = \mathbf{13}$.
* Left of 2: $2 - 1 = \mathbf{1}$.
* Below 21: $21 + 10 = \mathbf{31}$.
* Missing numbers:
* Left of 2: 1
* Below 2 (center of row 2): 12
* Right of 12: 13
* Left of 12 (above 21): 11
* Below 21: 31

Puzzle 3
* Given: 10 and 29.
* Shape:
* Row 1: [ ] [ ] [10]
* Row 2: [ ] [ ] [ ] (10 is above the rightmost box?)
* Row 3: [ ] [29] [ ]
* Row 4: [ ]
* Let's align them.
* 10 is at (Row 1, Col 3).
* Below 10 is (Row 2, Col 3): $10 + 10 = 20$.
* Below 20 is (Row 3, Col 3): $20 + 10 = 30$.
* We have 29 at (Row 3, Col 2).
* Check: Left of 30 is $30 - 1 = 29$. This matches!
* Now fill in the rest:
* Left of 10: $10 - 1 = \mathbf{9}$.
* Left of 9: $9 - 1 = \mathbf{8}$.
* Below 8 (Row 2, Col 1): $8 + 10 = \mathbf{18}$.
* Below 9 (Row 2, Col 2): $9 + 10 = \mathbf{19}$.
* Below 20 (Row 2, Col 3): 20 (calculated above).
* Left of 29 (Row 3, Col 1): $29 - 1 = \mathbf{28}$.
* Right of 29 (Row 3, Col 3): $29 + 1 = \mathbf{30}$.
* Below 28 (Row 4, Col 1): $28 + 10 = \mathbf{38}$.
* Missing numbers:
* Row 1: 8, 9
* Row 2: 18, 19, 20
* Row 3: 28, 30
* Row 4: 38

Puzzle 4
* Given: 25, 44.
* Shape:
* Row 1: [ ] [25]
* Row 2: [ ] [ ]
* Row 3: [44] [ ]
* Row 4: [ ]
* Alignment:
* 25 is at (Row 1, Col 2).
* Below 25 is (Row 2, Col 2): $25 + 10 = 35$.
* Below 35 is (Row 3, Col 2): $35 + 10 = 45$.
* We have 44 at (Row 3, Col 1).
* Check: Left of 45 is $45 - 1 = 44$. Matches!
* Fill in the rest:
* Left of 25: $25 - 1 = \mathbf{24}$.
* Left of 35 (Row 2, Col 1): $35 - 1 = \mathbf{34}$.
* Below 44 (Row 4, Col 1): $44 + 10 = \mathbf{54}$.
* Missing numbers:
* Row 1: 24
* Row 2: 34, 35
* Row 3: 45
* Row 4: 54

Puzzle 5
* Given: 68, 89.
* Shape:
* Row 1: [ ] [ ]
* Row 2: [ ] [68] [ ]
* Row 3: [ ] [ ]
* Row 4: [ ] [89]
* Wait, let's look closer at the image for Puzzle 5.
* Top row: Two boxes.
* Second row: Three boxes, middle is 68.
* Third row: Two boxes? No, looks like a box under the left of 68 and a box under the right of 68?
* Let's trace carefully.
* Center is 68.
* Left of 68: $68 - 1 = 67$.
* Right of 68: $68 + 1 = 69$.
* Above 67: $67 - 10 = 57$.
* Above 68? There is no box directly above 68. The top row has two boxes. They seem to be above 67 and 69? Or above 67 and 68?
* Looking at the lines: The top-left box is above the left-box of the second row (67). The top-right box is above the middle-box of the second row (68)? No, the vertical line separates them.
* Let's assume the top row corresponds to the first two columns of the second row.
* If Top-Right is above 68: $68 - 10 = 58$.
* If Top-Left is above 67: $67 - 10 = 57$.
* Now look at the bottom part.
* Third row: Has a box under 67? And a box under 68?
* Fourth row: Has 89.
* Let's find 89's neighbors.
* Above 89: $89 - 10 = 79$.
* Left of 89: $89 - 1 = 88$.
* Right of 89: $89 + 1 = 90$.
* Let's map the grid positions relative to 68 (Row 2, Col 2).
* (R2, C2) = 68.
* (R2, C1) = 67.
* (R2, C3) = 69.
* Top Row (R1): Boxes at C1 and C2? Or C2 and C3?
* Visually, the top-left box is above the gap between C1 and C2? No, it's above C1. The top-right box is above C2.
* So (R1, C1) = $67 - 10 = 57$.
* So (R1, C2) = $68 - 10 = 58$.
* Third Row (R3): Boxes at C1 and C2?
* Visually, there is a box under 67 (C1) and a box under 68 (C2)?
* Let's check the connection to 89.
* 89 is in the 4th row shown. It is aligned under the right-most box of the 3rd row?
* Let's look at the shape again.
* R1: [57] [58]
* R2: [67] [68] [69]
* R3: [77] [78] <-- Assuming boxes under 67 and 68.
* R4: [ ] [89]
* If 89 is at (R4, C2), then above it is (R3, C2) = 79.
* But if (R3, C2) is under 68, it should be $68 + 10 + 10 = 88$.
* Contradiction: $88 \neq 79$.
* Let's re-evaluate the position of 89.
* Maybe 89 is at (R4, C3)?
* If 89 is at (R4, C3), then above it is (R3, C3).
* (R3, C3) is under (R2, C3)=69. So (R3, C3) = 79.
* Then (R4, C3) = $79 + 10 = 89$. This works perfectly!
* So the structure is:
* R1: Boxes at C1, C2. Values: 57, 58.
* R2: Boxes at C1, C2, C3. Values: 67, 68, 69.
* R3: Boxes at C2, C3? Or C1, C2?
* Let's look at the drawing.
* Under 68 and 69?
* The box with 89 is on the far right of the bottom cluster.
* The box above 89 is empty.
* The box to the left of that empty box is filled.
* So R3 has boxes at C2 and C3.
* (R3, C3) is above 89. So (R3, C3) = $89 - 10 = 79$.
* (R3, C2) is left of 79. So (R3, C2) = $79 - 1 = 78$.
* Check vertical alignment for (R3, C2): It is under (R2, C2)=68. $68 + 10 = 78$. Matches!
* Check vertical alignment for (R3, C3): It is under (R2, C3)=69. $69 + 10 = 79$. Matches!
* Now back to Top Row (R1).
* The boxes are above (R2, C1) and (R2, C2)?
* Visually, the top block is shifted left compared to the bottom block?
* Let's look at the vertical lines.
* The left edge of the top-left box aligns with the left edge of the box containing 67. So Top-Left is above 67.
* The right edge of the top-right box aligns with the right edge of the box containing 68? Or does it align with the line between 68 and 69?
* Usually, these grids are consistent.
* If Top-Left is above 67 (C1), value is 57.
* If Top-Right is above 68 (C2), value is 58.
* Let's check the third row again.
* The drawing shows a box under 68 and a box under 69.
* So R3 C2 = 78, R3 C3 = 79.
* Then R4 has a box under R3 C3? Yes, that's 89.
* So the missing numbers are:
* Top-Left (above 67): 57
* Top-Right (above 68): 58
* Left of 68: 67
* Right of 68: 69
* Below 68: 78
* Below 69 (above 89): 79
* Left of 89: None (empty space in diagram).
* Wait, is there a box to the left of 89? The diagram shows a box to the left of the column containing 89?
* Let's look at Puzzle 5 image again.
* Row 3: Two boxes. One under 68, one under 69.
* Row 4: One box under the right box of Row 3 (which is 79). That box is 89.
* Is there a box to the left of 89? The diagram shows a blank space.
* So the missing numbers to fill in are:
* Top row: 57, 58
* Middle row sides: 67, 69
* Row below 68/69: 78, 79

Puzzle 6
* Given: 36.
* Shape:
* Row 1: [ ] [ ]
* Row 2: [ ] [36] [ ]
* Row 3: [ ] [ ]
* Alignment:
* 36 is at (R2, C2).
* Left of 36: $36 - 1 = \mathbf{35}$.
* Right of 36: $36 + 1 = \mathbf{37}$.
* Above 35 (R1, C1): $35 - 10 = \mathbf{25}$.
* Above 36 (R1, C2): $36 - 10 = \mathbf{26}$.
* Below 35 (R3, C1): $35 + 10 = \mathbf{45}$.
* Below 36 (R3, C2): $36 + 10 = \mathbf{46}$.
* Missing numbers:
* Row 1: 25, 26
* Row 2: 35, 37
* Row 3: 45, 46

Puzzle 7
* Given: 74.
* Shape:
* Row 1: [ ] [ ] [ ]
* Row 2: [74] [ ] [ ]
* Row 3: [ ] [ ] [ ]
* Row 4: [ ] (under the rightmost column?)
* Let's trace carefully.
* 74 is at (R2, C1).
* Right of 74 (R2, C2): $74 + 1 = \mathbf{75}$.
* Right of 75 (R2, C3): $75 + 1 = \mathbf{76}$.
* Above 74 (R1, C1): $74 - 10 = \mathbf{64}$.
* Above 75 (R1, C2): $75 - 10 = \mathbf{65}$.
* Above 76 (R1, C3): $76 - 10 = \mathbf{66}$.
* Below 74 (R3, C1): $74 + 10 = \mathbf{84}$.
* Below 75 (R3, C2): $75 + 10 = \mathbf{85}$.
* Below 76 (R3, C3): $76 + 10 = \mathbf{86}$.
* Row 4: There is one box. It is under the rightmost column (C3).
* Below 86 (R4, C3): $86 + 10 = \mathbf{96}$.
* Missing numbers:
* Row 1: 64, 65, 66
* Row 2: 75, 76
* Row 3: 84, 85, 86
* Row 4: 96

Puzzle 8
* Given: 29.
* Shape: Cross-like but extended.
* Row 1: [ ] [29] [ ]
* Row 2: [ ] [ ] [ ]
* Row 3: [ ] [ ] [ ]
* Row 4: [ ]
* Let's identify the center. 29 is at (R1, C2).
* Left of 29 (R1, C1): $29 - 1 = \mathbf{28}$.
* Right of 29 (R1, C3): $29 + 1 = \mathbf{30}$.
* Below 28 (R2, C1): $28 + 10 = \mathbf{38}$.
* Below 29 (R2, C2): $29 + 10 = \mathbf{39}$.
* Below 30 (R2, C3): $30 + 10 = \mathbf{40}$.
* Below 38 (R3, C1): $38 + 10 = \mathbf{48}$.
* Below 39 (R3, C2): $39 + 10 = \mathbf{49}$.
* Below 40 (R3, C3): $40 + 10 = \mathbf{50}$.
* Row 4: One box under the middle column (C2).
* Below 49 (R4, C2): $49 + 10 = \mathbf{59}$.
* Missing numbers:
* Row 1: 28, 30
* Row 2: 38, 39, 40
* Row 3: 48, 49, 50
* Row 4: 59

Puzzle 9
* Given: 87.
* Shape:
* Row 1: [ ] [ ]
* Row 2: [ ] [ ]
* Row 3: [ ] [ ]
* Row 4: [87] [ ]
* Let's align.
* 87 is at (R4, C1).
* Right of 87 (R4, C2): $87 + 1 = \mathbf{88}$.
* Above 87 (R3, C1): $87 - 10 = \mathbf{77}$.
* Above 88 (R3, C2): $88 - 10 = \mathbf{78}$.
* Above 77 (R2, C1): $77 - 10 = \mathbf{67}$.
* Above 78 (R2, C2): $78 - 10 = \mathbf{68}$.
* Above 67 (R1, C1): $67 - 10 = \mathbf{57}$.
* Above 68 (R1, C2): $68 - 10 = \mathbf{58}$.
* Missing numbers:
* Row 1: 57, 58
* Row 2: 67, 68
* Row 3: 77, 78
* Row 4: 88

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Final Answer:

1.
Top Row: 5, 7
Middle Row: 15, 17
Bottom Box: 35

2.
Top Left: 1
Middle Row: 11, 12, 13
Bottom Box: 31

3.
Top Row: 8, 9
Second Row: 18, 19, 20
Third Row: 28, 30
Bottom Box: 38

4.
Top Left: 24
Second Row: 34, 35
Third Row Right: 45
Bottom Box: 54

5.
Top Row: 57, 58
Middle Row Sides: 67, 69
Third Row: 78, 79

6.
Top Row: 25, 26
Middle Row Sides: 35, 37
Bottom Row: 45, 46

7.
Top Row: 64, 65, 66
Second Row Sides: 75, 76
Third Row: 84, 85, 86
Bottom Box: 96

8.
Top Row Sides: 28, 30
Second Row: 38, 39, 40
Third Row: 48, 49, 50
Bottom Box: 59

9.
Top Row: 57, 58
Second Row: 67, 68
Third Row: 77, 78
Bottom Right: 88