Question

Consider any positive four-digit integer that has all of its digits distinct and none equal to zero. What is the largest possible difference between such an integer and any integer that results from rearranging its digits

Answer 1

Answer:

Check the explanation.

Step-by-step explanation:

The highest four digit number is 9999 and lowest 4 digit number is 1000. The difference between them is (9999 - 1000) = 8999.

8999 cannot be difference according to the question, as here all the digits should be distinct rather than 0.

The difference between the 9 and 1 is 8, which is the highest difference among the unit digits rather than 0.

The 2nd lowest number after 9 is 8 and the 2nd highest unit digit after 1 is 2.

(8 - 2) = 6.

The difference will be highest if difference is calculated between the highest and lowest number.

With the 4 digits, 9, 8, 2, 1 the lowest number is 1289 and the highest number is 9821.

The difference is (9821 - 1289) = 8532.