Class 8 NCERT bridge course Answers Activity W6.7 Math Logic Puzzle Challenge

Students may be asked to solve the following puzzles. 

They may explain their logic of getting the solution

Supercell Swap Puzzle

 There is only one supercell (number greater than all its neighbours) in the following grid. If you exchange two digits from one of the numbers, there will be 4 supercells. Figure out which digits to swap.”

Answer:

Swap the digits 6 and 2 in 62,871 → it becomes 26,871.

Logic:

• Initially, only 62,871 is a supercell (greater than all 8 neighbors).

• After the swap, 62,871 becomes 26,871, which is no longer the greatest.

• Now, four different cells become local maxima (supercells), satisfying the condition.

2. Students may be asked ‘How many rounds does your birth year take to reach the kaprekar constant?

2. Kaprekar Constant Puzzle

“How many rounds does your birth year take to reach the Kaprekar constant?”

Instructions for students:

• Use your birth year (e.g., 1998).

• Rearrange digits to make the largest and smallest possible 4-digit numbers.

• Subtract the smaller from the larger.

• Repeat until you reach 6174 (Kaprekar's constant).

Example (for 1998):

1. 9981 − 1899 = 8082

2. 8820 − 0288 = 8532

3. 8532 − 2358 = 6174 
   Answer: 3 rounds

 

3. Students may be asked ‘Write one 5-digit number and two 3-digit numbers, such that their sum is 18,670.

3. Sum to 18,670

“Write one 5-digit number and two 3-digit numbers, such that their sum is 18,670.”

Answer Example:

• 5-digit number: 15,432

• 3-digit numbers: 1,765 and 1,473

Check:
15,432 + 1,765 + 1,473 = 18,670