Let's break down the problem:

You are given the digits: 2, 7, 9, 8, 4, and 3.

Jacob's Task (Smallest Possible Even Number):

• To create the smallest possible even number, Jacob needs to ensure the number ends with an even digit. The even digits available are 2, 4, and 8.
• To make the smallest possible number, he will choose the smallest digits first and place one of the even digits at the end.

The smallest even digit is 2, but if 2 is placed at the end, we would miss using 8 or 4 in a lower significant place. So, let’s try:

• Arrange the digits in increasing order: 2, 3, 4, 7, 8, 9.
• Now, place the smallest even digit at the end: 2, 3, 4, 7, 9, 8.

Thus, the smallest even number Jacob can form is 234798.

Isla's Task (Largest Possible Odd Number):

• To create the largest possible odd number, Isla needs to ensure the number ends with an odd digit. The odd digits available are 3, 7, and 9.
• To make the largest possible number, she will place the largest digits first and place the largest odd digit at the end.

Let’s arrange the digits in decreasing order: 9, 8, 7, 4, 3, 2.

• Now, place the largest odd digit at the end: 9, 8, 7, 4, 2, 3.

Thus, the largest odd number Isla can form is 987423.

Difference Between the Two Numbers:

• Jacob's number: 234798
• Isla's number: 987423

Now, subtract the smaller number from the larger number: $987423 - 234798 = 752625$

Conclusion:

The difference between the two numbers is 752625.

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Would you like further details or have any other questions? Here are five follow-up questions to deepen your understanding:

1. How would the difference change if the digits were arranged to make different even or odd numbers?
2. Can you explain how the parity of a number affects its classification as even or odd?
3. What strategy could Jacob use to ensure he always gets the smallest even number?
4. How do the place values of digits impact the size of the number?
5. What if Jacob and Isla had one more digit to use—how would that change the problem?

Tip: When forming the smallest or largest number, always start by focusing on the most significant digits (leftmost), as they contribute the most to the magnitude of the number.