Explore Take different 4-digit numbers and try carrying out these steps. Find out what happens. Check with your friends what they got.

Question

Homi · Accepted Answer

We follow the steps in the diagram to see what number we get.

Step 1 — Start with a number

Let us pick a 4-digit number. We will use the number 1234.

We make the largest number from its digits. We call this A. $A = 4321$

We make the smallest number from its digits. We call this B. $B = 1234$

Now, we subtract B from A. We call this C. $C = A - B$ $C = 4321 - 1234$

$\boxed{C = 3087}$

Diagram 1

Step 2 — Repeat with C

Now we use the digits of C, which is 3087.

We make the largest number from these digits. $A = 8730$

We make the smallest number from these digits. Remember to put zero first. $B = 0378$

Now, we subtract B from A. $C = A - B$ $C = 8730 - 0378$

$\boxed{C = 8352}$

Step 3 — Repeat again

Now we use the digits of C, which is 8352.

We make the largest number from these digits. $A = 8532$

We make the smallest number from these digits. $B = 2358$

Now, we subtract B from A. $C = A - B$ $C = 8532 - 2358$

$\boxed{C = 6174}$

Step 4 — Final check

Now we use the digits of C, which is 6174.

We make the largest number from these digits. $A = 7641$

We make the smallest number from these digits. $B = 1467$

Now, we subtract B from A. $C = A - B$ $C = 7641 - 1467$

$\boxed{C = 6174}$

If we keep doing this with 6174, we will always get 6174.

Answer

When we follow these steps, we always reach the number 6174. Once we reach 6174, we will always get 6174 if we repeat the steps. This number 6174 is special. It is called the Kaprekar constant.

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