Class 8 NCERT bridge course Answers Activity W6.2 What Makes a Super Cell?" — A Logical Number Puzzle

  Activity W 6.2 

What Makes a Super Cell?" — A Logical Number Puzzle

Understanding the Activity

Students are shown a table of numbers. Some of the numbers are colored, and students must reason out why.

We define the colored cells as super cells — but the rule behind why they're super cells is hidden. Students must infer the logic.

Students may observe and discuss the reason, behind these activities. 

Procedure 

 Students may be asked to observe the numbers written in the table below. 

 They may tell, why some numbers are coloured. Discuss.

Possible Rule Behind Super Cells:

• Prime numbers

• Palindromes (e.g. 626)

• Numbers divisible by 3 or 7

• Numbers with repeated digits

• Numbers where the sum of digits equals 10

• Even numbers above 500

Encourage students to come up with creative or patterned rules, then challenge peers to figure them out.

Let us call the cells that are coloured as super cells. 

Students may be asked to create their own tables and ask the other students to reason it out. 

They may be allowed to use some other variations in this puzzle, as well.

Extension 

Students may create their own tables and ask their friends to colour or mark super cells in it. 

For example 

6828 670 9435 3780 3708 7308 8000 5583 52 

 Students may discuss on the following: 

 Fill the table below such that we get as many super cells as possible. 

Fill a table with as many super cells as possible (100–999, no repeats).

→ Use a clear rule like “multiples of 11” or “numbers ending in 7.” Example:

121 132 143 154
165 176 187 198

Here, all could be super cells based on a consistent rule.

Use numbers between 100 and 1000 without any repetition. 

 Can you fill a supercell table, without repeating numbers, such that there are no supercells? Why or why not? 

Yes, you can fill a supercell table without repeating numbers such that there are no supercells — but only if the numbers you choose do not satisfy the supercell rule.

Explanation:

A supercell is defined by a hidden rule (like being prime, a multiple of 5, a palindrome, etc.). If you intentionally choose numbers that do not satisfy the rule, then there will be no supercells.

Example:

Suppose the rule is:
"A supercell is any number that is divisible by 3."

Now fill your table with numbers between 100 and 999 that are not divisible by 3:

101 103 104 106  

107 110 112 113  
115 118 121 122  
124 127 128 131

• No numbers here are divisible by 3.

• Therefore, no supercells appear, and the rule is preserved.

•  No numbers are repeated.

Why This Is Possible:

Because the supercell status depends entirely on the rule, you can avoid it by carefully choosing numbers that break the rule.

 Yes, it is possible — if you know or guess the rule and avoid it intentionally.

2. Can you fill a table with no super cells?

Yes — if you choose a rule that no number in the table meets.
Example: Rule = “Palindromes only”, but you don’t include any palindromes (e.g., no 121, 131, etc.)

 Will the cell with the largest number always be a super cell?

No — only if your rule involves being "the largest" or exceeding a threshold.

Can the smallest number be a super cell? Why or why not?

 Yes — if it fits the rule. For instance, if 109 is prime or has a digit sum of 10, it could be a super cell.

Fill a table where the 2nd largest number is not a super cell.

 Yes — make sure the rule excludes it.
E.g., if the rule is “even numbers,” and the 2nd largest number is odd.

 Fill a table such that the cell having the second largest number is not a supercell but the second smallest number is a supercell. Is it possible?

 

Yes, it is possible to fill a table such that:

• The second largest number is not a supercell, and

• The second smallest number is a supercell.

How This Works:

Whether a number is a supercell depends on a specific rule, such as:

• Is it a prime number?

• Is it divisible by 5?

• Is the sum of digits equal to 10?

• Is it a palindrome?

You can select numbers carefully so that:

• The second largest number does not satisfy the rule (so it's not a supercell),

• The second smallest number does satisfy the rule (so it is a supercell).

Example Table (Rule: Supercell = Number is a Prime Number)

[127, 118, 199, 305]  
[109, 134, 211, 187]  
[149, 203, 101, 299]  
[97, 223, 158, 293]

• Sorted values: 97, 101, 109, 118, 127, 134, 149, 158, 187, 199, 203, 211, 223, 293, 299, 305

• Second smallest = 101 →  Prime → Supercell

• Second largest = 299 →  Not Prime → Not a Supercell

So this satisfies the condition.

Yes, it's entirely possible. You just need to:

• Choose a supercell rule,

• Ensure the second smallest value fits the rule, and

• Ensure the second largest value doesn’t.

Can the 2nd largest number not be a super cell but the 2nd smallest number is?

Yes — just choose numbers accordingly and apply a rule that includes one and excludes the other.