Chapter 3 — Number Play

Chapter 3 uses numbers to explore patterns, puzzles, and games. Topics include supercells (numbers larger than all neighbours in a table), palindromes, the Kaprekar constant 6174, the Collatz Conjecture, digit sums, and simple estimation — all building 'computational thinking' skills.

A supercell is a cell in a number table whose value is greater than ALL its adjacent cells. In a single row, adjacent means left and right neighbours. The largest number in any table is always a supercell; the smallest can never be one.

The Kaprekar constant for 4-digit numbers is 6174. Take any 4-digit number with at least two different digits, arrange its digits to form the largest number (A) and smallest number (B), then subtract B from A. Repeat with the result — you always reach 6174. For 3-digit numbers, the constant is 495.

Start with any whole number. If it is even, halve it; if it is odd, multiply by 3 and add 1. Repeat. The conjecture (stated in 1937 by Lothar Collatz) says you will always eventually reach 1, no matter which number you start with. It has never been proven for all numbers and remains an unsolved problem.

A palindromic number reads the same from left to right and right to left. Examples from Ganita Prakash Chapter 3: 66, 575, 797, 848, 1111, 10001, 99999. The reverse-and-add method (add a number to its reverse) eventually produces a palindrome for all 2-digit numbers.

The digit '7' appears 20 times in numbers 1 to 100: 10 times in the units place (7, 17, 27, 37, 47, 57, 67, 77, 87, 97) and 10 times in the tens place (70 through 79). In 1 to 1000, it appears 300 times.

The digit sum of a number is found by adding all its digits. For example, 68 has digit sum 6+8=14, and 176 has digit sum 1+7+6=14. The smallest number with digit sum 14 is 59 (5+9=14). The largest 5-digit number with digit sum 14 is 95,000.

In Game #1, the first player says 1, 2, or 3, and players alternate adding 1, 2, or 3 to reach 21. The first player can always win by controlling key positions: after saying 1 first, always bring the running total to 5, 9, 13, 17, and finally 21 (positions differing by 4).

There are 90,000 five-digit numbers (10,000 to 99,999). The pattern: 1-digit = 9, 2-digit = 90, 3-digit = 900, 4-digit = 9,000, 5-digit = 90,000. Each tier has 9 times as many numbers as the previous.

Yes, the NCERT Ganita Prakash Class 6 textbook PDF is freely available from the official NCERT website. No sign-up is required to download it from NCERT's portal.

The largest 5-digit palindrome is 99,999 and the smallest is 10,001. Their difference is 99,999 – 10,001 = 89,998. Their sum is 99,999 + 10,001 = 1,10,000.

The chapter's summary describes computational thinking as 'thinking about and formulating set procedures to use numbers for these purposes' — whether to convey information, find patterns, estimate, solve puzzles, or develop game strategies. It is a key skill developed through the activities in this chapter.