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A Quickie, not tricky (Posted on 2015-05-11) Difficulty: 1 of 5
How many ordered sets of positive integers are there if:

1.Their sum is less than 6
2. There are at most 4 addends
3. None of them is composite.

Please specify how quick were you to get the right answer.

No Solution Yet Submitted by Ady TZIDON    
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Hints/Tips re(3): Solution spoiler.....Now list them ALL! | Comment 5 of 6 |
(In reply to re(2): Solution spoiler.....Now list them ALL! by Dej Mar)

There are two main kinds of set:  
   unordered sets, and ordered sets

An unordered set is just a list of numbers, for example; {1, 2, 3, 4, 5} is the set of natural counting numbers from 1 to 5. Mathematically, it wouldn't have made any difference if I had written {3, 1, 5, 2, 4} instead, since this is still the same set of numbers, regardless of the order I write them in.

In an ordered set, on the other hand; the order in which each number appears is important, and may even determine what each number in the set means. For example, if a point on a map has coordinates (10, 42), the number 10 might refer to the horizontal co-ordinate on the map, and then the number 42 would be the vertical co-ordinate on the map. If I swap the numbers and write (42, 10) instead; this is obviously a different place on the map.

The above (copied and pasted) relates to the answer provided by the solver:

the five sets {1,1}, {1,2}, {1,3}, {2,2}, {2,3}, actuallyimply

eight ordered sets {1,1}, {1,2}, {1,3}, {2,2}, {2,3},{2,1},{3,1},{3,2}, in similar way you should recount the triplets and the quadruplets.

  Posted by Ady TZIDON on 2015-05-11 12:00:22
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