Figure-Based Number Patterns

🎯 Learning Objective

Solve boxes and figures where corner or diagonal numbers combine to give a central value.

💡 Concept

• Boxes place numbers at the four corners with one number in the centre
• The centre is built from the corners — test: sum of all four, top-pair vs bottom-pair, or the two diagonals
• Common rules: centre = sum of corners; centre = (top-left×top-right) + (bottom-left×bottom-right)
• Diagonal rule: centre = (top-left × bottom-right) − (top-right × bottom-left)
• Two complete boxes confirm the rule; the third is solved by applying it
• Always fix a reading order (TL, TR, BL, BR) so you compare like with like

🧮 Key Formulas

Centre = TL + TR + BL + BR

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Centre = (TL × TR) + (BL × BR)

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Centre = (TL × BR) − (TR × BL)

✏️ Easy Example

Q. Boxes with corners (TL, TR, BL, BR) and a centre: (3,4,5,6)→18, (2,6,1,5)→14, (4,3,7,2)→?. Find the centre.

1. Try sum of the four corners: 3+4+5+6 = 18 ✓
2. Confirm: 2+6+1+5 = 14 ✓
3. Apply: 4+3+7+2

Answer: 16

🇮🇳 Real-Life Example

A shopkeeper totalling four corners of a bill into one grand total is doing this exact figure sum — the centre is just the running total of what surrounds it.

📝 Exam-Level Example

Q. Boxes with corners (TL, TR, BL, BR)→centre: (2,3,4,5)→26, (1,4,2,6)→16, (3,3,2,5)→?. Find the centre.

1. Plain sum fails (2+3+4+5 = 14, not 26)
2. Try (TL×TR) + (BL×BR): 2×3 + 4×5 = 6 + 20 = 26 ✓, 1×4 + 2×6 = 4 + 12 = 16 ✓
3. Apply: 3×3 + 2×5 = 9 + 10

Answer: 19

📝 Exam-Level Example

Q. Boxes with corners (TL, TR, BL, BR)→centre: (8,3,2,4)→26, (6,2,3,5)→24, (7,4,2,3)→?. Find the centre.

1. Try the diagonals: (TL×BR) − (TR×BL)
2. 8×4 − 3×2 = 32 − 6 = 26 ✓, 6×5 − 2×3 = 30 − 6 = 24 ✓
3. Apply: 7×3 − 4×2 = 21 − 8

Answer: 13

🪄 Memory Trick

Run three quick checks in order: sum of all four → product of pairs → diagonal difference. One of the three fits almost every RRB figure question.

⚠️ Common Mistakes

• ❌ Reading the four corners in a different order in each box — fix TL, TR, BL, BR everywhere
• ❌ Stopping at 'sum' and missing product- or diagonal-based rules
• ❌ Confusing which pair multiplies — top with top, bottom with bottom (not top with bottom)

🏆 Exam Tips

• ✅ Note the numbers' size: a large centre with small corners screams multiplication
• ✅ Test your rule on BOTH given boxes before committing to the answer

📌 Summary

• Centre is built from the corner numbers
• Check sum → product of pairs → diagonal difference
• Fix a corner-reading order for every box
• Confirm the rule on both complete figures