Question 4

We will follow the steps in the diagram. We will use 3-digit numbers. We will find a repeating number.

Step 1 — First calculation

Let us pick a 3-digit number. We choose 123. Its digits are 1, 2, and 3. We make the largest number (A). $A = 321$ We make the smallest number (B). $B = 123$ We subtract B from A. This gives C. $C = A - B$ $C = 321 - 123$

$\boxed{C = 198}$

Step 2 — Second calculation

Now we use the digits of C. C is 198. Its digits are 1, 9, and 8. We make the largest number (A). $A = 981$ We make the smallest number (B). $B = 189$ We subtract B from A. This gives C. $C = A - B$ $C = 981 - 189$

$\boxed{C = 792}$

Step 3 — Third calculation

Now we use the digits of C. C is 792. Its digits are 7, 9, and 2. We make the largest number (A). $A = 972$ We make the smallest number (B). $B = 279$ We subtract B from A. This gives C. $C = A - B$ $C = 972 - 279$

$\boxed{C = 693}$

Step 4 — Fourth calculation

Now we use the digits of C. C is 693. Its digits are 6, 9, and 3. We make the largest number (A). $A = 963$ We make the smallest number (B). $B = 369$ We subtract B from A. This gives C. $C = A - B$ $C = 963 - 369$

$\boxed{C = 594}$

Step 5 — Fifth calculation

Now we use the digits of C. C is 594. Its digits are 5, 9, and 4. We make the largest number (A). $A = 954$ We make the smallest number (B). $B = 459$ We subtract B from A. This gives C. $C = A - B$ $C = 954 - 459$

$\boxed{C = 495}$

Step 6 — Sixth calculation

Now we use the digits of C. C is 495. Its digits are 4, 9, and 5. We make the largest number (A). $A = 954$ We make the smallest number (B). $B = 459$ We subtract B from A. This gives C. $C = A - B$ $C = 954 - 459$

$\boxed{C = 495}$ The number 495 is repeating.

Answer

The number that will start repeating is 495.