Maths Subject Enrichment Activity (Class 8)

Chapter / Theme

BOX LABEL INSIDE COLOUR
RED 🔵 Blue
BLUE 🟢 Green
GREEN 🔴 Red

Logical Reasoning & Problem Solving
(Ganita Prakash – Part 2, Puzzle-Based Thinking)

Title of the Activity

🎨 Find the Colours! – One-Box Logic Puzzle

Topic

Logical reasoning, elimination method, deductive thinking

Aim

To develop logical reasoning skills by solving a real-life puzzle using minimum information and systematic elimination.

Learning Outcomes

Students will be able to:

Apply logical reasoning to solve puzzles
Understand the concept of incorrect labeling
Use elimination and deduction strategies
Explain reasoning clearly in words

Materials Required

Three closed boxes
Coloured balls (Red, Blue, Green)
Labels marked RED, BLUE, GREEN
Pen and notebook (for observation & reasoning)

Given Situation

There are 3 closed boxes:
- One contains only red balls
- One contains only blue balls
- One contains only green balls
Each box is labeled RED, BLUE, GREEN
Important Condition: ❌ No box has the correct label
You are allowed to open only one box
Task: Find the correct colour for all three boxes

Procedure

Carefully read the condition that all labels are wrong.
Choose any one box to open.
Observe the colour of the balls inside.
Use logical reasoning to reassign correct labels to:
- The opened box
- The remaining two unopened boxes
Record the reasoning step-by-step.

Observation

Suppose we open the box labeled RED.

Since no box is correctly labeled, the RED-labeled box cannot contain red balls.
If we observe blue balls inside:
- The RED label is wrong → confirmed
- So this box must be BLUE
Now consider the remaining boxes:
- Box labeled BLUE cannot be blue
- Box labeled GREEN cannot be green
Using elimination:
- BLUE-labeled box → must be GREEN
- GREEN-labeled box → must be RED

Result / Conclusion

✅ By opening just one box, we can correctly identify the contents of all three boxes.

This is possible because:

All labels are incorrect
Logical elimination gives a unique solution

Final Correct Labelling (Example Case)

Original Label	Actual Colour
RED	BLUE
BLUE	GREEN
GREEN	RED

(Answer may vary depending on which box is opened, but the logic remains the same.)

Mathematical Reasoning Used

Elimination
Deductive logic
Case analysis
Constraint-based reasoning

Reflection

Opening more than one box is unnecessary
Careful thinking reduces effort
Logic puzzles strengthen decision-making skills

Higher Order Thinking Skills (HOTS)

Why is it essential that all labels are wrong?
What happens if one label is correct?
Can you solve this puzzle if there are 4 boxes and 4 colours?
How is this puzzle similar to solving equations?

Real-Life Connection

Sorting and classification problems
Error detection in labeling systems
Decision-making with limited information

SOLUTION – Find the Colours!

Given

Three boxes contain only one colour each:
🔴 Red balls 🔵 Blue balls 🟢 Green balls
Boxes are labelled RED, BLUE, GREEN
❌ No box has the correct label
Only one box can be opened

🔍 Step-by-Step Logical Solution

Step 1: Open ONE box

Open the box labelled RED.

Step 2: Observe the colour inside

Suppose the box contains BLUE balls.

Since all labels are wrong, the box labelled RED
❌ cannot contain red balls
❌ cannot match its label

✅ Therefore, this box must actually be the BLUE box.

Step 3: Relabel the opened box

RED label → actually contains BLUE balls

Step 4: Deduce the remaining two boxes

Now only RED and GREEN colours remain.

The box labelled BLUE ❌ cannot contain blue balls
The box labelled GREEN ❌ cannot contain green balls

So:

BLUE label → GREEN balls
GREEN label → RED balls

✅ Final Correct Arrangement

Box Label	Actual Colour
RED	🔵 Blue
BLUE	🟢 Green
GREEN	🔴 Red

🧠 Why This Works

Every label is wrong → strong constraint
Opening one box gives enough information
Remaining boxes are solved using elimination

✨ Key Mathematical Idea

Logical Deduction & Elimination

📝 Student Conclusion (Model Answer)

By opening only one box and using the condition that all labels are incorrect, we can logically determine the correct colours of all three boxes.

🔥 HOTS – Ready Answers

Q1. Why can’t we open more than one box?
👉 It is unnecessary; one box gives complete information.

Q2. What if one label was correct?
👉 The puzzle would have multiple answers or no unique solution.

Q3. What type of thinking is used here?
👉 Logical reasoning and elimination.

TEACHER ANSWER KEY

Find the Colours!

Class: VIII
Book: Ganita Prakash – Part 2
Type: Logical Reasoning / Puzzle-based Enrichment Activity

🧠 Correct Solution (For Teacher Reference)

Given Conditions

Three boxes contain only one colour each:
- 🔴 Red balls
- 🔵 Blue balls
- 🟢 Green balls
Boxes are labelled RED, BLUE, GREEN
❌ No box has the correct label
✔ Only one box may be opened

📌 Step-by-Step Logical Reasoning

Step 1: Choose one box to open

Open the box labelled RED.

Step 2: Observe the colour

Assume the box labelled RED contains BLUE balls.


┌──────────────┐
│  Label: RED  │
│  Inside: 🔵  │
└──────────────┘

Step 3: Apply the condition

The label RED is incorrect (given)
So this box cannot contain red balls
✔ Therefore, this box must be the BLUE box

Step 4: Deduce remaining boxes

Now colours left are RED and GREEN

Box labelled BLUE ❌ cannot contain blue
Box labelled GREEN ❌ cannot contain green

So logically:


BLUE label  → 🟢 GREEN balls
GREEN label → 🔴 RED balls

✅ Final Correct Matching (Answer Table)

Box Label	Actual Colour
RED	🔵 Blue
BLUE	🟢 Green
GREEN	🔴 Red

🧩 Diagram-Based Summary (Board Explanation)


Initially (All labels wrong):

[ RED ]   [ BLUE ]   [ GREEN ]
  ?          ?          ?

Open RED box → 🔵

Therefore:
[ RED ] → 🔵
Remaining colours: 🔴, 🟢

[ BLUE ] → 🟢
[ GREEN ] → 🔴

🎯 Mathematical Concepts Assessed

Logical reasoning
Elimination method
Deductive thinking
Constraint-based problem solving

📝 Expected Student Conclusion