he 25 Breakdown ake the number 25 and break it up into as many pieces as you wan
ID: 3114314 • Letter: H
Question
he 25 Breakdown ake the number 25 and break it up into as many pieces as you want. For example 25 10 10+5 25 2 + 23 qb,s4P Your challenge is to answer the following questions: s 1. How can you write 25 as the sum of positive integers so that the product of those integers is as large as possible? Describe the process you used to come up with your answer. Why do you think your answer is the best? 2. How can you write 25 as the sum of positive integers so that the product of those integers is as small as possible? Describe the process you used to come up with your answer 3. What if you're allowed to use negative numbers (for instance, 25 -1 26), how can you write 25 so that the product of the numbers you used is as large as possible? Describe the process you used to come up with your answer 4. If you're again allowed to use negative numbers, what's the smallest product you can make? Describe the process you used to come up with your answer. ur answers to these questions should be detailed - walk me through your thinking, Describe y you tried different combinations and provide examples of combinations you tried before ming to your final answer ere are 'correct" answers to all of the questions above, but you don't necessarily need to fi m to get full credit (though it couldn't hurt), What's more important is the level of thought tail, and effort you put into your responses.Explanation / Answer
if the sum is of 2 numbers then
25 = a + b
ab should be largest so
f = a*b = a*(25-a)
f' = 25 - 2a = 0
a = 12.5
so product = 12.5
similarly if you choose 3 numbers, the maximum of product will occur at 25/3*25/3*25/3
If (this product of 3 numbers is less than product of 2 numbers, then the combination of 3 integer numbers will also be less than numbers). Find below the table to get a rough idea at first how many split would give the maximum product -
The answer has to be 8,9,10,11,12
8 splits = (3^7)*4 = 8748
9 splits = (3^8)*1 = 6561
10 splits = (2^9)*7 = 3584
11 splits = (3^8)*1 = 5120
12 splits = (3^8)*1 = 6144
So 8 splits is the maximum (3,3,3,3,3,3,3,4)
1 25 25 2 13 156 3 8 579 4 6 1526 5 5 3125 6 4 5233 7 4 7411 8 3 9095 9 3 9846 10 3 9537 11 2 8356 12 2 6685 13 2 4920 14 2 3352 15 2 2127 16 2 1262 17 1 704 18 1 370 19 1 184 20 1 87 21 1 39 22 1 17 23 1 7 24 1 3 25 1 1Related Questions
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