What is the difference between the smallest 6-digit number with five different digits and the greatest 5-digit number with four different digits?

For the smallest 6-digit number with five different digits:

The lakh's place cannot be 0. Place 1 (smallest non-zero) at the lakh's place. Use 0 in as many remaining positions as possible. To have exactly five different digits, we need three more digits besides 1 and 0. The smallest such digits are 2, 3 and 4.

Total six digits: 1, 0, 0, 2, 3, 4 — five different digits (1, 0, 2, 3, 4).

Arranging with 1 at the lakh's place and the rest in ascending order:

Smallest 6-digit number = 1,00,234.

For the greatest 5-digit number with four different digits:

Use 9 as many times as possible. Use 9 twice, then the next three largest different digits are 8, 7 and 6.

Total five digits: 9, 9, 8, 7, 6 — four different digits (9, 8, 7, 6).

Arranging in descending order:

Greatest 5-digit number = 99,876.

Difference = 1,00,234 - 99,876

= 358

Hence, the required difference is 358.