Swapping digits

In your book, Maths Mela (Chapter 1), there is a game called 'Digit swap'. You take a number and interchange (swap) any two of its digits. For example, in 1,478, swapping the 7 and the 4 gives 1,748.

Which digit matters most? The one on the far left, because it is in the biggest place. To make 1,478 larger than 5,500, we need a big digit in the thousands place. Swap the 1 and the 8: we get 8,471, which is more than 5,500. Swapping the 1 and the 7 also works: 7,418.

Now take 10,593 and try to make a number between 11,000 and 15,000. It must start with 1 and then a thousands digit of 1, 2, 3 or 4. Swap the 0 and the 3: we get 13,590. That is between 11,000 and 15,000. To go above 35,000, put a big digit in the ten-thousands place: swap the 1 and the 5 to get 50,193, or the 1 and the 9 to get 90,513.

To make a number as BIG as possible, bring the biggest digit to the front. In 48,247, swap the 4 and the 8: 84,247. To make it as SMALL as possible, bring the smallest digit to the front. Swap the first 4 and the 2: 28,447. (A 0 can never go in front, because then the number would lose a place.)