- Let the four unknown numbers be A, B, C, and D, arranged as:
- Top-left: A
- Top-right: B
- Bottom-left: C
- Bottom-right: D
- The equations from the image are:
1. A + B = 10
2. C - D = 12
3. A + C = 17
4. B + D = 10
- From equation (1): B = 10 - A
- From equation (3): C = 17 - A
- Substitute B and C into equations (2) and (4):
Equation (2): (17 - A) - D = 12 → D = 17 - A - 12 → D = 5 - A
Equation (4): (10 - A) + D = 10 → D = 10 - (10 - A) → D = A
- Now set the two expressions for D equal:
5 - A = A → 5 = 2A → A = 2.5
- Substitute back to find the others:
B = 10 - 2.5 = 7.5
C = 17 - 2.5 = 14.5
D = A = 2.5
- Verify all equations:
- A + B = 2.5 + 7.5 = 10 ✓
- C - D = 14.5 - 2.5 = 12 ✓
- A + C = 2.5 + 14.5 = 17 ✓
- B + D = 7.5 + 2.5 = 10 ✓
- Final values:
- Top-left: 2.5
- Top-right: 7.5
- Bottom-left: 14.5
- Bottom-right: 2.5
Parent Tip: Review the logic above to help your child master the concept of riddle math.
