>>>>>Sum=(N^3)/6+(N^2)/2+N/3
>>>>>If this is right, I will send you bill ::)
>>>>
>>>>Ladies and gents, we have a winner! That is, converting, the same as my solution of Gifts = n * (n+1) * (n+2) / 6. Congratulations, Edward!
>>>
>>>OK, Bruce, you've done it again. It's like a song I can't stop singing in my head.
>>>
>>>if my Algebra II memory serves me right, the proper way to write this formula is:
>>>
>>>n * (n+1) * (n+2)
>>>-----------------
>>> (1*2*3)
>>>
>>>what kind of problem is this?
>>
>>It's combinatorics, at least that's how I solved it:
>>
>> (n+2) (n+2)! (n+2)(n+1)n
>>C = ----------------- = ------------------,
>> (n-1) (n-1)! (n+2-(n-1)! 3!
>>
>>after canceling like terms of factorials.
>
>Well, since Edward already solved it I won't press on, especially since time is a premium right now. :-)
>
>However, this excercise brings up an interesting thought. We are extremely dependent on computer machinations to solve our problems for us, and rightly so since many of them can only be solved thru numeric analysis. Nevertheless, it still seems better to use a closed form solution to a problem if it exists for both expediency and the excercise of the mind, :-)
>
>Bill

Types of problems like this fall into the category of cardinality. Some can't be solved without knowing the theory, since there is no "brute force" method. For example: You and your most significant other decide that for simplicity's sake you're only going to exchange 5 gifts, from a list of 52 (one for each week). Come Christmas morning, how many distinct possibilities (including opening order) are there?

George