5th Grade Math - Teach You to Think Every Day

Author: Chai Changlong
Publisher:
Publish Date: 2006-08-01
Features: On Thursday, break down 14 into the sum of several natural numbers and then find the product of these numbers. What is the maximum product?
Pointers: To maximize the product of the natural numbers that sum up to 14, it's best to break it down into as many numbers as possible, but avoid using 1. The number of 2s should not exceed two. For example, breaking 6 into 2+2+2 and calculating 2×2×2 gives a product of 8, which is less than breaking it into 3+3, yielding 3×3=9. Additionally, the numbers should not exceed 4. For instance, if a number like 5 appears, it should be further broken down into 2 and 3, since 2×3>5. Based on this analysis, it's best to break down the number into as many 3s as possible.
Solution: 14 = 3+3+3+3+2, with a product of 3×3×3×3×2=162 being the maximum.
Showtime!
1. Break down 17 into the sum of several natural numbers and find the product. What is the maximum product?
2. If you break down 16 into the sum of different digits, how should you arrange them to maximize the product of these different digits?