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Number Play is the chapter many Class 6 students enjoy most, and it is also where careless slips hide. The puzzles look like games, but each one trains a skill you will use for years: following a rule exactly, spotting a pattern and asking whether it always holds. This post works through the three most famous puzzles in the chapter with real numbers, shows where students go wrong, and ends with a practice plan.
What is in the Number Play chapter?
Chapter 3 of Ganita Prakash, NCERT's Class 6 mathematics book (first edition August 2024, now in its 2026-27 reprint), runs through twelve short sections. They include digit sums, palindromes, the "magic number" of Kaprekar, clock and calendar numbers, mental maths, the Collatz conjecture, estimation, and games with winning strategies.
The chapter summary names the skill it is after: thinking about and setting up procedures that use numbers, which it calls "computational thinking". It also makes a point worth remembering. Many problems about numbers are easy to state but very hard to solve, and some are still unsolved.
What is a palindrome, and what does reverse-and-add do?
A palindrome reads the same from left to right and right to left, such as 66, 848 or 1111. The chapter gives a procedure: start with a 2-digit number, add it to its reverse, and repeat until you get a palindrome.
Worked example 1. Start with 68.
68 + 86 = 154
154 + 451 = 605
605 + 506 = 1111, a palindrome after 3 steps.
Some numbers are slow. Starting from 89 takes 24 steps and ends at 8813200023188. Try the first few steps yourself: 89 + 98 = 187, 187 + 781 = 968, 968 + 869 = 1837.
The book says every 2-digit start does reach a palindrome, but for 3-digit numbers the answer is unknown, and it is suspected that 196 never does. The On-Line Encyclopedia of Integer Sequences lists 196 as the first of the numbers that apparently never give a palindrome under reverse-and-add. "Apparently" is the honest word: nobody has proved it either way.
How does Kaprekar's 6174 work?
The chapter introduces D. R. Kaprekar as a mathematics teacher at a government school in Devlali, Maharashtra, who discovered this pattern in 1949. Take any 4-digit number with at least two different digits.
Arrange the digits from largest to smallest. Call it A.
Arrange them from smallest to largest. Call it B.
Find C = A − B, and repeat with C.
Worked example 2 (from the book). Start with 6382.
8632 − 2368 = 6264
6642 − 2466 = 4176
7641 − 1467 = 6174
Once you reach 6174, it repeats: 7641 − 1467 = 6174 again. The number is now called Kaprekar's constant. The same encyclopedia lists 495 and 6174 among the fixed points of this mapping: numbers that the routine turns back into themselves. The book rules out numbers such as 3333, whose digits are all the same, because A − B would be 0 and the routine would stop there.
Worked example 3 (the zero trap). The book asks how many rounds 5683 takes. Watch the second line.
8653 − 3568 = 5085
8550 − 0558 = 7992
9972 − 2799 = 7173
7731 − 1377 = 6354
6543 − 3456 = 3087
8730 − 0378 = 8352
8532 − 2358 = 6174
That is 7 rounds. In round 2, B must be 0558, keeping the zero as a digit. If you write 558 and treat it as a 3-digit number, the process goes wrong.
The chapter also asks you to try 3-digit numbers. Start with 352: 532 − 235 = 297, then 972 − 279 = 693, then 963 − 369 = 594, then 954 − 459 = 495. From there, 954 − 459 = 495 again, so 495 repeats.
What is the Collatz conjecture?
The rule is short: if a number is even, halve it; if it is odd, multiply by 3 and add 1. The book's first example starts at 12: 12, 6, 3, 10, 5, 16, 8, 4, 2, 1.
The chapter says Lothar Collatz conjectured in 1937 that the sequence always reaches 1, whatever whole number you start with, and that this is still unsolved. A conjecture is a statement that looks true but has not been proved. Checking many numbers is evidence, not proof, and that difference is one of the most useful ideas a Class 6 student can meet.
Which mistakes should you watch for?
Dropping zeros in Kaprekar's routine. Always write four digits.
Reversing only part of a number. The reverse of 154 is 451, not 145.
Odd and even confusion in Collatz. Check the last digit before choosing the rule.
Stopping too early. A number like 1001 is a palindrome; 1011 is not.
Treating examples as proof. Ten cases that work do not show that every case works.
How should you practise this week?
Day 1: Run reverse-and-add on every 2-digit number from 50 to 59 and record the steps.
Day 2: Pick three 4-digit numbers, including one with a zero, and count Kaprekar rounds.
Day 3: Try five 3-digit numbers in the 3-digit version and see what repeats.
Day 4: Write Collatz sequences for 7, 9 and 27, and note the largest number each reaches.
Day 5: Write one sentence for each puzzle explaining what you noticed and whether you can say why.
If you get stuck on why a rule works, the Fermi Concept Library covers every concept in physics, chemistry, biology, mathematics and computing, so you can read up on an idea before returning to the puzzle. The book opens with these habits in its first chapter, which our post on patterns in mathematics in Class 6 covers, and they carry on into prime time in Class 6.
Pick the year you were born, add a digit to make four if you need one, and see how many rounds it takes to reach 6174.
