Maths Class 6 Important Questions Chapter 3 Ganita Prakash

Number Play

1. In the table below, mark the supercells (cells having a number greater than all their adjacent cells).

Answer:

A supercell is the cell with a number larger than all its adjacent cells. For example, in the second row, “8000” is a supercell as it’s greater than its adjacent cells: 7308, 5583, 7854, and 3708.

2. Place the following numbers on a number line:
2180, 2754, 1500, 3600, 9950, 5300, 8400.

Answer:

• First, draw a number line starting from 1000 to 10,000 with equal intervals (e.g., intervals of 1000).
• Plot the points at appropriate locations based on the given numbers.

3. Find all 3-digit numbers whose digit sums are 12. Write down any four such numbers.

Answer:
Some examples of numbers whose digits add up to 12:

384 (3 + 8 + 4 = 12)

741 (7 + 4 + 1 = 12)

936 (9 + 3 + 6 = 12)

654 (6 + 5 + 1 = 12)

4. Write down all 3-digit palindromes that use the digits 1, 2, and 3.

Answer:

The 3-digit palindromes using the digits 1, 2, and 3 are:

• 121, 131, 232, 323, 222, 333.

5. Pick a 4-digit number, arrange the digits to form the largest and smallest numbers, subtract them, and repeat the process until you reach Kaprekar’s constant (6174).

Answer:
For example:

• Start with 4321.
• Largest number: 4321, Smallest number: 1234.
• Subtract: 4321 – 1234 = 3087.
• Repeat the process with 3087: 8730 – 0378 = 8352.
• 8532 – 2358 = 6174 (Kaprekar’s constant).

6. Apply the Collatz Conjecture starting with 25. Follow the steps (if even, divide by 2; if odd, multiply by 3 and add 1) until you reach 1.

Answer:

• Start with 25 (odd): 25 × 3 + 1 = 76.
• 76 (even): 76 ÷ 2 = 38.
• 38 (even): 38 ÷ 2 = 19.
• 19 (odd): 19 × 3 + 1 = 58.
• Continue until you reach 1.

7. Estimate the number of words in a page of your maths textbook. If one page contains approximately 250 words, estimate how many words are in the whole book (assuming there are 100 pages).

Answer:

• If one page has 250 words, and the book has 100 pages, then the total number of words is approximately:
  250 × 100 = 25,000 words.

8. Write two 3-digit numbers whose digits add up to the same value. Then, find the digit sums and check your results.

Example Answer:

• Numbers: 176 and 367.
  • 1 + 7 + 6 = 14
  • 3 + 6 + 7 = 16
• Another example could be: 245 (2 + 4 + 5 = 11) and 523 (5 + 2 + 3 = 10).

9. Create a 5-digit palindromic number using the digits 1, 3, and 5. Write any two possible numbers.

Answer:

• Example palindromes: 13531, 53335.

10. What is the sum of the largest and smallest 5-digit palindrome? Also, find their difference.

Answer:

• The smallest 5-digit palindrome is 10001, and the largest is 99999.
• Sum: 10001 + 99999 = 110000.
• Difference: 99999 – 10001 = 89998.

11. Apply the Collatz Conjecture starting with the number 15. Show the sequence until you reach 1.

Answer:

• Start with 15 (odd): 15 × 3 + 1 = 46.
• 46 (even): 46 ÷ 2 = 23.
• 23 (odd): 23 × 3 + 1 = 70.
• Continue until you reach 1.

12. Estimate the number of steps you would take to walk from your classroom to the school gate. If your school gate is 200 meters away and each step covers about 0.5 meters, how many steps will it take?

Answer:

• Number of steps = 200 ÷ 0.5 = 400 steps.

13. Use the numbers 25,000; 13,000; 400; and 1,500 to form different sums that equal 38,800 and 31,000. Show your workings.

Answer:

• 38,800 = 25,000 + 13,000 + 400 × 2.
• 31,000 = 25,000 + 1,500 × 4.

14. The time now is 7:07. How many minutes will pass before the next palindromic time?

Answer:

• The next palindromic time after 7:07 is 8:08.
• Difference in time = 8:08 – 7:07 = 61 minutes.

15. Choose a 4-digit number (with different digits), and use Kaprekar’s steps to reach the constant 6174. For example, start with 4321.

Answer:

• Start with 4321: Largest number = 4321, Smallest number = 1234.
• Subtract: 4321 – 1234 = 3087.
• Repeat the process: 8730 – 0378 = 8352.
• Continue until you reach 6174.

16. Using the numbers 210 and 390, create a number pattern that sums to exactly one of these numbers. Write the pattern.

Answer:

• Pattern for 210:
  10 + 20 + 30 + 40 + 50 + 60 = 210.