Problem Analysis:
The image shows the number
508 represented using matchsticks. The task is to rearrange exactly
2 matches to form the largest possible number.
Step-by-Step Solution:
1.
Understand the Current Configuration:
- The number
508 is formed using matchsticks.
- The digit
5 is made with 5 matchsticks.
- The digit
0 is made with 6 matchsticks.
- The digit
8 is made with 7 matchsticks.
2.
Objective:
- Move exactly 2 matches to create the largest possible number.
3.
Strategy:
- To maximize the number, we should aim to:
1. Increase the leftmost digits (since they have the highest place value).
2. Use as many digits as possible to form a larger number.
3. Avoid creating invalid digits (e.g., non-standard representations).
4.
Exploration of Moves:
-
Digit 5: The digit
5 can be transformed into other digits by moving matches. For example:
- Moving 2 matches can turn
5 into
9.
-
Digit 0: The digit
0 is stable and does not easily transform into another digit without breaking its structure.
-
Digit 8: The digit
8 is also stable and does not easily transform into another digit without breaking its structure.
5.
Optimal Transformation:
- Transforming the
5 into a
9 is a good starting point because it increases the value of the leftmost digit.
- After transforming the
5 into a
9, we are left with the digits
908. However, we still have 2 matches to move.
- To further increase the number, we can use these 2 matches to add a new digit. The best choice is to create a
1, as it is the smallest digit and requires only 2 matches.
6.
Final Configuration:
- Move 2 matches from the
5 to turn it into a
9.
- Use the remaining 2 matches to create a
1 at the end of the number.
- The resulting number is
9081.
Verification:
- The original number is
508.
- By moving 2 matches, we transformed the
5 into a
9.
- We used the remaining 2 matches to create a
1.
- The new number is
9081, which is the largest possible number achievable with the given constraints.
Final Answer:
$$
\boxed{9081}
$$
Parent Tip: Review the logic above to help your child master the concept of solutions to brain teasers.
