Kevin will start with the integers 1, 2, 3 and 4 each used exactly once and written in a row in any order. Then he will find the sum of the adjacent pairs of integers in each row to make a new row, until one integer is left. For example, if he starts with 3, 2, 1, 4, then he takes sums to get 5, 3, 5, followed by 8, 8, and he ends with the final sum 16. Including all of Kevin's possible starting arrangements of the integers 1, 2, 3 and 4, how many possible final sums are there?

Hello,there are 5 differents sums:16,18,20,22,24.-------------------------------------------------------Dim i As Integer, j As Integer, k As Integer, l As Integer, u As Integer, v As Integer, nb As IntegerDim mat(4, 4) As Integernb = 0For i = 1 To 4    For j = 1 To 4        If j <> i Then            For k = 1 To 4                If k <> j And k <> i Then                    l = 10 - k - j - i                    If l > 0 And l < 5 And l <> i And l <> j And l <> k Then                        mat(1, 1) = i                        mat(1, 2) = j                        mat(1, 3) = k                        mat(1, 4) = l                        For u = 2 To 4                            For v = 1 To 4 - u + 1                                mat(u, v) = mat(u - 1, v) + mat(u - 1, v + 1)                            Next v                        Next u                        'Call visu(mat())                        nb = nb + 1                        Print nb,                        mat(4, 1)                    End If                End If            Next k        End If    Next jNext iEndSub visu (m() As Integer)    Dim i As Integer, j As Integer    For i = 1 To 4        For j = 1 To 4 - i + 1            Print m(i, j);        Next j        Print    Next iEnd Sub