Here's something to develop

Lets say you have a group of numbers, all distinct.

They are represented by an equation, lets say G = C1+C2+C3...+Cn

Such that G is a group of N integer elements such that there sum is mTargVal.
The N elements are distinct, ie... each one of them is not equal to any other of them.

Lets say that the smallest element in the group G = mCellLow,
and the largest element is mCellHigh.

For Example, lets say that N = 6
and mCellLow = 0
and mCellHigh = 18
and mTargVal = 16

1. Determine a fucntion that tightens the limits...mCellLow and mCellHigh
2. Determine a function that returns what values MUST BE USED in this range.

In the example that I gave to you, you will see that:

If 5 of the numbers are 0 1 2 3 4, {The smallest set of N-1 numbers available} that the maximal mCellHigh really could be is 6.

This is because if you add the N-1 lowest possible values together, you have created the most minimal sum that N-1 of those elements can add to.

Which, if you then subtract from the targvl, you see that the most maximal value of a c could be only 6.

So the real range that mCellLow and mCellHigh could be is 0 and 6.

Using this as an example, and any others that you can think of, I am certain you can acheive #1.


Now, Number 2 is a bit more complex, however, when all is said and done, it is a very simple function.

Try by hand the following example:

Using 5 distinct numbers, 3 <= Cn <= 18
and those 5 numbers add to 27

What numbers MUST be used?
{BTW, this examples solution has tightened the C Limits}

{I will provide more examples in the morning, but the answer to this is:

You Are Required to use numbers in the range : 3 <= C <= 9
3 Numbers Ascending {Inclusive} from 3 { 3 -> 5 }
To Add To 27
When you must use 5 Numbers GTE 3 and LTE 9
Once and only once

}

Are you really asking for someone to develop this or just trying to show off your math?

As for point number 1, you can logically deduce that mCellLow must always be 0, which makes mCellHigh ridiculously easy to calculate.

No interest expressed.

Alright then.

Code:

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    Public Function DETERMINE_TARGVALS_CELL_MIN_MAX(ByRef mCellLow As Integer, ByRef mCellHigh As Integer, ByVal mTargVal As Integer, ByVal mBaseCellCount As Integer) As Boolean
        Dim mBaseCellCount_m1 As Integer = mBaseCellCount - 1
        Dim mBaseCellCount_m2 As Integer = mBaseCellCount - 2
        Dim mBaseCellCount_PackedSum As Integer = (mBaseCellCount_m1 * mBaseCellCount_m2) / 2

        Dim mTemp As Integer = mTargVal - mCellLow * mBaseCellCount_m1 - mBaseCellCount_PackedSum
        If mCellHigh > mTemp Then
            mCellHigh = mTemp
        End If

        mTemp = mTargVal - mCellHigh * mBaseCellCount_m1 + mBaseCellCount_PackedSum
        If mCellLow < mTemp Then
            mCellLow = mTemp
        End If

        If mCellLow > mCellHigh Then
            Return False
        End If

        Return True
    End Function
    Public Function DETERMINE_MUST_USE_RANGES(ByRef mCellLow As Integer, ByRef mCellHigh As Integer, ByVal mTargVal As Integer, ByVal mBaseCellCount As Integer, _
                                                ByRef mMustUseLowCount As Integer, ByRef mMustUseHighCount As Integer, ByRef mFreeCells As Integer) As Boolean

        Dim mAdjustedTargVal As Integer = mTargVal - mBaseCellCount * mCellLow
        Dim mAdjustedLowCell As Integer = 0
        Dim mAdjustedHighCell As Integer = mCellHigh - mCellLow

        Dim mAbsoluteMinVal As Integer = (mBaseCellCount * (mBaseCellCount - 1)) / 2
        Dim mAbsoluteMaxVal As Integer = mBaseCellCount * mAdjustedHighCell - mAbsoluteMinVal

        Dim mLowDifference As Integer = madjustedTargVal - mAbsoluteMinVal
        Dim mHighDifference As Integer = mAbsoluteMaxVal - mAdjustedTargVal

        mMustUseLowCount = mBaseCellCount - mLowDifference
        mMustUseHighCount = mBaseCellCount - mHighDifference

        If mMustUseLowCount < 0 Then
            mMustUseLowCount = 0
        End If
        If mMustUseHighCount < 0 Then
            mMustUseHighCount = 0
        End If

        'mFreeCells = mBaseCellCount - mMustUseLowCount - mMustUseHighCount
        'If mFreeCells < 0 Then
        '    mFreeCells = 0
        'End If
        'error conditions?

        If mMustUseLowCount > mBaseCellCount Then
            Return False
        End If
        If mMustUseHighCount > mBaseCellCount Then
            Return False
        End If
        'IS there any way that, if either of the MustUseCounts equals mbasecellcount, the other doesn't?

        Return True
    End Function

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