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Class 6 Number Play: cheat sheet
CBSE Mathematics. Playing with digits: supercells, palindromes, Kaprekar’s routine and the Collatz sequence, digit sums, and estimating.
Key ideas
- A supercell holds a number bigger than all its neighbours.
- A palindrome reads the same both ways: 121, 4334. Reversing a number and adding often leads to one.
- Kaprekar’s routine: arrange a 4-digit number’s digits largest-first and smallest-first and subtract; repeating always reaches 6174 (if the digits are not all the same).
- Collatz: if a number is even, halve it; if odd, multiply by 3 and add 1. Every number tried so far reaches 1.
- Estimate by rounding, then check whether the exact answer is close.
Remember
| Kaprekar step | largest arrangement − smallest arrangement |
| Kaprekar’s constant | 6174 (7641 − 1467 = 6174) |
| Collatz rule | even → n ÷ 2; odd → 3n + 1 |
Watch out
- Dropping a leading zero in Kaprekar’s routine: if a step gives 999, keep it as 0999 so it still has four digits.
- Stopping a sequence one step too early.
- Calling a number a palindrome when only its first and last digits match.
Worked example
Start Kaprekar's routine with 5320. Write each subtraction until you reach 6174.
Working: 5320 − 0235 = 5085; 8550 − 0558 = 7992; 9972 − 2799 = 7173; 7731 − 1377 = 6354; 6543 − 3456 = 3087; 8730 − 0378 = 8352; 8532 − 2358 = 6174
Answer: 7 steps
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