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Concept 6 of 8

Building Numbers: Before, After & Biggest

Free
1

Today's big idea

Big digits belong in the big places, and a number can never start with 0.

Greatest is digits sorted downwards; smallest is upwards, with 0 moved off the front.

2

How it works

👀 What's going on?

Hand a friend four digit cards and ask for the biggest number they can build. Most people shuffle the cards around and hope. There is a rule that gets it right first time, and one trap that catches nearly everybody.

💡 Here's the trick

Digits: 8 · 3 · 5 · 18351Greatest ▸ big to small8531= 8,531Smallest ▸ small to big1358= 1,358

Look at the two builds above. The same four digits make the greatest number when the biggest digit takes the leftmost place, and the smallest number when the smallest digit leads. Every place to the left is worth more, so that is where the big digits belong.

🪄 How to do it

  1. 1.Sort your digits biggest to smallest, the way the builds above are arranged.
  2. 2.That order is the greatest number, and reversing it gives the smallest.
  3. 3.If 0 is your smallest digit, swap it with the next one up, because a number cannot start with 0.

✍️ Try it

Use the digits 2, 7, 0 and 5 once each. What is the greatest number you can make, and what is the smallest?

Biggest first gives 7, 5, 2, 0, so the greatest is 7,520. Smallest first would give 0, 2, 5, 7, but a number cannot open with 0. Swap the first two and the smallest is 2,057.

⚠️ Watch out

You might be thinking the smallest number is just the greatest one written backwards. With a 0 among your digits it is not. 0257 is not a four-digit number at all, so the 0 has to move one place right and sit second.

🌟 Why this matters

Picking the best price, the top score or the fastest time is the same move: decide which digit deserves the biggest place. You reason it out instead of guessing.
Exam tip: Greatest-and-smallest questions are a Class 3 favourite, and the 0 trap is the whole point of them.

3

Watch me solve one

Quanta solves it

“Watch how I think through one of these — then you try.”

THE PROBLEM

“Using the digits 7, 2, 9, 4 once each, make the greatest 4-digit number.”

  1. 1

    Greatest → biggest first

    For the biggest number, put the largest digit in the highest place. 🏗️

  2. 2

    Sort the digits high to low

    7, 2, 9, 4 sorted downward → 9, 7, 4, 2.

  3. 3

    Read them off

    9 · 7 · 4 · 2 = 9,742

  4. 4

    Built ✓

    Greatest = 9,742

Now you try one — same steps, different story 👇

4

See it in action

⚡ Time to play!

Predecessor = 1 less. Greatest → biggest digit first. Smallest → smallest first (0 never leads).

BUILD · ROUND 1 OF 3

Build the PREDECESSOR of 6,000 (the number that comes just before it).

Tap the digits to fill the four slots.

ThHTO

Digit pool — tap to place

5

Quick check

✅ VERIFICATION

Using the digits 5, 0, 8, 3 once each, what is the SMALLEST 4-digit number you can make?

⚡ Finish the activity above first to answer.

Keep going!

Up next: The Abacus

Each rod is a place value, read and build any number.

Concept 7 of 8 →