Form two four-digit numbers from the digits 2, 3, 4, 5, 6, 7, 8,
and 9, using each digit exactly once, so that the absolute value of
the difference of the two numbers is as small as possible.
Confused need to double check with you all.
9753-8642=1111
i was wrong! sorry...
So far, I think it's 6234-5987 to get a difference of 247...
To form two four-digit numbers using the given digits (2, 3, 4, 5, 6, 7, 8, 9), you need to consider a few steps:
Step 1: Start by sorting the digits in descending order. This ensures that the resulting numbers are as close in value as possible.
Digits: 9, 8, 7, 6, 5, 4, 3, 2
Step 2: Place the largest digit (9) in the thousands place of one of the numbers. To maximize the difference between the two numbers, place the next largest digit (8) in the thousands place of the other number.
Options:
The first number is 9000, and the second number is 8000.
The first number is 8000, and the second number is 9000.
Step 3: For the remaining six digits, divide them equally into groups of three. Make sure each group contains digits in descending order. Assign one group to each number, ensuring that the digit order provides the smallest difference possible.
Options:
Group 1: 7, 6, 5
Group 2: 4, 3, 2
Number 1: 7576 and Number 2: 8432
Number 1: 7685 and Number 2: 7432
Step 4: Calculate the absolute difference between the two numbers and choose the option with the smallest difference.
Option 1 (9000 - 8000) = 1000
Option 2 (8432 - 7576) = 856
Option 3 (8000 - 9000) = 1000
Option 4 (7685 - 7432) = 253
Based on these calculations, the absolute difference is smallest when you form the numbers 7685 and 7432.
Therefore, the two four-digit numbers with the smallest absolute difference are 7685 and 7432.