Number Play | Mathematics Grade 6 CBSE

Play with it

Six number tricks

Numbers hide patterns and surprises. Tap each term to see the trick behind it and try it on numbers of your own.

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The three big ideas

Place value tells you what each digit is worth. In 4,732 the 4 is 4000, the 7 is 700, the 3 is 30 and the 2 is 2.
Largest number from a set of digits: place the biggest digit on the left (highest place value), then the next biggest, and so on.
Smallest number: smallest digits first – but a number cannot start with 0, so the smallest non-zero digit goes first.
The digit sum is just all the digits added: 4 + 7 + 3 + 2 = 16. It is the start of many number tricks.

Worked example. Using the digits 7, 0, 4, 2 once each, make the largest and the smallest 4-digit numbers.

Step 1. Order the digits: 0 < 2 < 4 < 7.

Step 2. Largest – biggest digit first: 7, 4, 2, 0 = 7420.

Step 3. Smallest – smallest first, but not 0 at the front: 2, 0, 4, 7 = 2047.

Write numbers in a row of cells. A supercell is a cell whose number is larger than each of its neighbours – a local peak.
In the row 3 | 9 | 5 | 8 | 2 , the supercells are 9 (bigger than 3 and 5) and 8 (bigger than 5 and 2).
The first and last cells have only one neighbour, so they are supercells only if they beat that single neighbour.
Puzzle idea: can you arrange numbers so there are as many supercells as possible? They must alternate high–low–high, because two supercells can never sit side by side.

Common mistake: calling the biggest number in the whole row "the supercell". A row can have several supercells – each one only has to beat its own neighbours, not every number.

Palindromes read the same both ways: 121, 1331, 45654. Take any number, reverse it, add the two – repeat and you often reach a palindrome.
Kaprekar's constant 6174: take a 4-digit number with at least two different digits. Arrange its digits largest-to-smallest, then smallest-to-largest, and subtract. Repeat – you always reach 6174, discovered by Indian mathematician D. R. Kaprekar.
Clever estimation: round numbers to a nearby tidy value to add or compare them fast in your head before working out the exact answer.

Worked example. Run Kaprekar's routine on 1234.

Step 1. 4321 − 1234 = 3087.

Step 2. 8730 − 0378 = 8352.

Step 3. 8532 − 2358 = 6174 – and from here it never changes.

Where you'll meet it

Number play at work

Quick mental maths at a shop

Rounding ₹297, ₹488 and ₹206 to ₹300, ₹500 and ₹200 tells you the bill is about ₹1000 before the shopkeeper finishes adding – a fast check that you are not being overcharged.

Codes, PINs & lucky numbers

Arranging digits to make the biggest or smallest value, or spotting palindrome dates like 12-02-2021, is the same digit-juggling you do here – useful for memorable codes and number games.

Puzzles & brain training

Kaprekar's 6174 and supercell hunts are the kind of puzzles that sharpen logical thinking – the same skill that makes Sudoku, magic squares and competitive maths feel easy.

Check yourself

Competency quiz

Modelled on the competency-based pattern — MCQ, assertion–reason and a case study, testing whether you can use the ideas, not just recall them.

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