Sums of Sets of Prime NumbersDate: 01/07/2003 at 21:56:20 From: Molly Subject: High school puzzle Given several sets of prime numbers, use each of the nine non-zero digits exactly once. What is the smallest possible sum such a set could have? An example would be the set: {5, 29,43, 67, 81}. Their sum is 225 but this is not the smallest sum. The smallest sum I was able to find was 207 using the set {61, 47, 2, 89, 35}. I am told this is not correct. Date: 01/08/2003 at 14:07:18 From: Doctor Ian Subject: Re: High school puzzle Hi Molly, The first thing that occurs to me is to get the prime digits alone by themselves: {2, 3, 5, 7} 1, 4, 6, 8, 9 Now what can we do with the remaining digits? 41 is prime, and so is 89: {2, 3, 5, 7, 41, 89} 6 6 isn't prime, so maybe we can attach it to another number. Can you see how to do that? But is this the _smallest_ possible sum? Well, let's consider a few things. There is no way that 4, 6, or 8 can appear in the unit place of a prime number. (Do you see why?) So those are all going to have to appear as parts of combined numbers. 9 can't appear by itself; and right now we have it in the units position, so we can only make things worse by doing anything else with it. So are there any changes that you could make to this set that would make the sum smaller? Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ Date: 01/08/2003 at 21:23:35 From: Molly Subject: Thank you (High school puzzle) Thank you for taking the time to answer my question. I greatly appreciate it! I found your hints to be very helpful. I think your website is great. Keep up the great work. Thanks again, Molly McS. |
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