4th Grade Math Puzzles - Free Printable

Final Answer:
Top row (left to right):
- First triangle: missing circle = 11, rectangle = 42 (already given), bottom-left circle = 20, bottom-right circle = 22 → top circle = 13 = 20 + 11? Wait — re-read rule.

Wait! Rule says: *“The numbers in the circles added together makes the number in the linking rectangle.”*
So: two circles connected to a rectangle → their sum = rectangle value.
Also, each triangle has:
- Top circle
- Two middle squares (connected to top circle and bottom circles)
- Bottom three: left circle — rectangle — right circle
But looking at first triangle:
Top circle = 13
Left square = 33
Bottom-left circle = 20
Rectangle = 42
Bottom-right circle = 22

How are they linked? From diagram:
- Top circle connects to two squares (left and right).
- Each square connects down to one bottom circle and to the rectangle.
- The rectangle is between the two bottom circles.

Crucially: “The numbers in the circles added together makes the number in the linking rectangle.”
So rectangle = sum of the two bottom circles.
Check first triangle: 20 + 22 = 42 ✔ matches rectangle.

Also, each square connects top circle and one bottom circle — likely: square = top circle + bottom circle? Let’s test:
Left square = 33, top = 13, bottom-left = 20 → 13 + 20 = 33 ✔
Right square = ? should be 13 + 22 = 35
So missing right square = 35.

Now apply this consistently:

Rule summary:
- Rectangle = left bottom circle + right bottom circle
- Left square = top circle + left bottom circle
- Right square = top circle + right bottom circle

Let’s verify with another known triangle:
Second triangle (top = 18, bottom-left = 14, bottom-right = 17)
→ rectangle should be 14 + 17 = 31
→ left square = 18 + 14 = 32
→ right square = 18 + 17 = 35
So missing: left square = 32, rectangle = 31, right square = 35

Third triangle (top = 20, bottom-left = 16, bottom-right = 17)
→ rectangle = 16 + 17 = 33
→ left square = 20 + 16 = 36
→ right square = 20 + 17 = 37

Now fill all missing blanks using this rule.

We’ll go triangle by triangle:

1. Triangle 1: top=13, left circle=20, right circle=22, rect=42 (given), left square=33 (given)
→ right square = 13 + 22 = 35

2. Triangle 2: top=18, left circle=14, right circle=17
→ left square = 18+14 = 32
→ rectangle = 14+17 = 31
→ right square = 18+17 = 35

3. Triangle 3: top=20, left circle=16, right circle=17
→ left square = 20+16 = 36
→ rectangle = 16+17 = 33
→ right square = 20+17 = 37

4. Triangle 4: top=31, left circle=22, right circle=14
→ left square = 31+22 = 53
→ rectangle = 22+14 = 36
→ right square = 31+14 = 45

5. Triangle 5: top=18, left circle=25, right circle=17
→ left square = 18+25 = 43
→ rectangle = 25+17 = 42
→ right square = 18+17 = 35

6. Triangle 6: top=24, left circle=9, right circle=35
→ left square = 24+9 = 33
→ rectangle = 9+35 = 44
→ right square = 24+35 = 59

7. Triangle 7: top=15, left square=27, right circle=17
We know: left square = top + left circle → 27 = 15 + left circle → left circle = 12
Rectangle = left circle + right circle = 12 + 17 = 29
Right square = top + right circle = 15 + 17 = 32

8. Triangle 8: top=31, right square=46, left circle=25
Right square = top + right circle → 46 = 31 + right circle → right circle = 15
Rectangle = left circle + right circle = 25 + 15 = 40
Left square = top + left circle = 31 + 25 = 56

9. Triangle 9: left square=31, right square=29, left circle=23
We have:
left square = top + left circle → 31 = top + 23 → top = 8
right square = top + right circle → 29 = 8 + right circle → right circle = 21
Rectangle = left circle + right circle = 23 + 21 = 44

Now list all missing values in order as they appear (left to right, top to bottom):

Triangle 1: right square = 35
Triangle 2: left square = 32, rectangle = 31, right square = 35
Triangle 3: left square = 36, rectangle = 33, right square = 37
Triangle 4: left square = 53, rectangle = 36, right square = 45
Triangle 5: left square = 43, rectangle = 42, right square = 35
Triangle 6: left square = 33, rectangle = 44, right square = 59
Triangle 7: left circle = 12, rectangle = 29, right square = 32
Triangle 8: right circle = 15, rectangle = 40, left square = 56
Triangle 9: top circle = 8, right circle = 21, rectangle = 44

But the worksheet has exactly 18 blank boxes (squares and circles). Let's count blanks in image layout:

Row 1: 3 triangles — blanks:
- T1: 1 blank (right square)
- T2: 3 blanks (left square, rectangle, right square)
- T3: 3 blanks
→ 7 so far

Row 2: 3 triangles — each has 3 blanks → 9 → total 16

Row 3: 3 triangles —
- T7: 3 blanks (left circle, rectangle, right square)
- T8: 3 blanks (left square, rectangle, right circle)
- T9: 3 blanks (top circle, rectangle, right circle)
→ 9 more → total 25? That seems off.

Better: Actually, look at each triangle has 3 blanks typically (two squares + rectangle, or circles + square etc). But from given numbers, we can extract exact blank positions.

Instead, provide answer as a list per triangle in reading order, filling only the blank cells:

Let me reconstruct each triangle with blanks labeled:

1) Top=13, left sq=33, left circ=20, rect=42, right circ=22 → missing: right sq = 35

2) Top=18, left circ=14, right circ=17 → missing: left sq, rect, right sq → 32, 31, 35

3) Top=20, left circ=16, right circ=17 → missing: left sq, rect, right sq → 36, 33, 37

4) Top=31, left circ=22, right circ=14 → missing: left sq, rect, right sq → 53, 36, 45

5) Top=18, left circ=25, right circ=17 → missing: left sq, rect, right sq → 43, 42, 35

6) Top=24, left circ=9, right circ=35 → missing: left sq, rect, right sq → 33, 44, 59

7) Top=15, left sq=27, right circ=17 → missing: left circ, rect, right sq → 12, 29, 32

8) Top=31, right sq=46, left circ=25 → missing: left sq, rect, right circ → 56, 40, 15

9) Left sq=31, right sq=29, left circ=23 → missing: top circ, rect, right circ → 8, 44, 21

So final answer is the list of all missing numbers in order left-to-right, top-to-bottom as they appear on the page:

35, 32, 31, 35, 36, 33, 37, 53, 36, 45, 43, 42, 35, 33, 44, 59, 12, 29, 32, 56, 40, 15, 8, 44, 21

But that’s 25 numbers — maybe some are not blank. Let's count actual blanks in the image description: Each triangle has 3 empty shapes. 9 triangles → 27 positions. Given numbers fill some.

Given numbers:
T1: top(13), left sq(33), left circ(20), rect(42), right circ(22) → 5 given → 3 blanks? No, triangle has 5 elements: top circle, 2 squares, 2 bottom circles, and 1 rectangle = 6 elements. But rectangle is central linking, so total 6 per triangle. In T1, 5 given, 1 blank (right square). So 1 blank.

T2: top(18), left circ(14), right circ(17) → 3 given → 3 blanks (2 squares + rectangle)

T3: top(20), left circ(16), right circ(17) → 3 given → 3 blanks

T4: top(31), left circ(22), right circ(14) → 3 given → 3 blanks

T5: top(18), left circ(25), right circ(17) → 3 given → 3 blanks

T6: top(24), left circ(9), right circ(35) → 3 given → 3 blanks

T7: top(15), left sq(27), right circ(17) → 3 given → 3 blanks

T8: top(31), right sq(46), left circ(25) → 3 given → 3 blanks

T9: left sq(31), right sq(29), left circ(23) → 3 given → 3 blanks

Total blanks = 1 + 3×8 = 25 blanks.

So 25 answers.

But the instruction says: “Find the missing numbers in this puzzle.” and “Provide only the final correct answer.”

To avoid ambiguity, output the missing numbers in order as they appear left-to-right, top-to-bottom, each blank filled:

1. Triangle 1, right square: 35
2. Triangle 2, left square: 32
3. Triangle 2, rectangle: 31
4. Triangle 2, right square: 35
5. Triangle 3, left square: 36
6. Triangle 3, rectangle: 33
7. Triangle 3, right square: 37
8. Triangle 4, left square: 53
9. Triangle 4, rectangle: 36
10. Triangle 4, right square: 45
11. Triangle 5, left square: 43
12. Triangle 5, rectangle: 42
13. Triangle 5, right square: 35
14. Triangle 6, left square: 33
15. Triangle 6, rectangle: 44
16. Triangle 6, right square: 59
17. Triangle 7, left circle: 12
18. Triangle 7, rectangle: 29
19. Triangle 7, right square: 32
20. Triangle 8, left square: 56
21. Triangle 8, rectangle: 40
22. Triangle 8, right circle: 15
23. Triangle 9, top circle: 8
24. Triangle 9, rectangle: 44
25. Triangle 9, right circle: 21

Thus final answer is these 25 numbers in order:

35, 32, 31, 35, 36, 33, 37, 53, 36, 45, 43, 42, 35, 33, 44, 59, 12, 29, 32, 56, 40, 15, 8, 44, 21

But since the format says “Provide only the final correct answer”, I'll give that list.

Final Answer:
35, 32, 31, 35, 36, 33, 37, 53, 36, 45, 43, 42, 35, 33, 44, 59, 12, 29, 32, 56, 40, 15, 8, 44, 21