Printable Math Puzzles - Free Printable

Problem Description:

The image shows an "Arithmogon Triangle Puzzle" where the numbers in the circles are added together to form the number in the triangle below them. The task is to find the missing numbers in the puzzle.

Key Rules:

1. Each triangle's value is the sum of the two numbers in the circles above it.
2. Use the given numbers and relationships to solve for the missing values.

Step-by-Step Solution:

#### Top Row:
1. First Triangle (13):
- Circles: 7, ?
- Equation: \( 7 + ? = 13 \)
- Solve: \( ? = 13 - 7 = 6 \)

2. Second Triangle (15):
- Circles: ?, 8
- Equation: \( ? + 8 = 15 \)
- Solve: \( ? = 15 - 8 = 7 \)

3. Third Triangle (19):
- Circles: ?, 10
- Equation: \( ? + 10 = 19 \)
- Solve: \( ? = 19 - 10 = 9 \)

#### Second Row:
4. First Triangle (17):
- Circles: 6, ?
- Equation: \( 6 + ? = 17 \)
- Solve: \( ? = 17 - 6 = 11 \)

5. Second Triangle (14):
- Circles: ?, 7
- Equation: \( ? + 7 = 14 \)
- Solve: \( ? = 14 - 7 = 7 \)

6. Third Triangle (23):
- Circles: ?, 9
- Equation: \( ? + 9 = 23 \)
- Solve: \( ? = 23 - 9 = 14 \)

#### Third Row:
7. First Triangle (22):
- Circles: 11, ?
- Equation: \( 11 + ? = 22 \)
- Solve: \( ? = 22 - 11 = 11 \)

8. Second Triangle (21):
- Circles: ?, 7
- Equation: \( ? + 7 = 21 \)
- Solve: \( ? = 21 - 7 = 14 \)

9. Third Triangle (37):
- Circles: ?, 14
- Equation: \( ? + 14 = 37 \)
- Solve: \( ? = 37 - 14 = 23 \)

#### Fourth Row:
10. First Triangle (33):
- Circles: 11, ?
- Equation: \( 11 + ? = 33 \)
- Solve: \( ? = 33 - 11 = 22 \)

11. Second Triangle (35):
- Circles: ?, 14
- Equation: \( ? + 14 = 35 \)
- Solve: \( ? = 35 - 14 = 21 \)

12. Third Triangle (60):
- Circles: ?, 23
- Equation: \( ? + 23 = 60 \)
- Solve: \( ? = 60 - 23 = 37 \)

#### Fifth Row:
13. First Triangle (55):
- Circles: 22, ?
- Equation: \( 22 + ? = 55 \)
- Solve: \( ? = 55 - 22 = 33 \)

14. Second Triangle (58):
- Circles: ?, 21
- Equation: \( ? + 21 = 58 \)
- Solve: \( ? = 58 - 21 = 37 \)

15. Third Triangle (97):
- Circles: ?, 37
- Equation: \( ? + 37 = 97 \)
- Solve: \( ? = 97 - 37 = 60 \)

Final Answer:

The missing numbers in the puzzle are:
\[
\boxed{6, 7, 9, 11, 7, 14, 11, 14, 23, 22, 21, 37, 33, 37, 60}
\]