Question

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?

Answer 1

Hello,

there are 5 differents sums:

16,18,20,22,24.

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Dim i As Integer, j As Integer, k As Integer, l As Integer, u As Integer, v As Integer, nb As Integer

Dim mat(4, 4) As Integer

nb = 0

For 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 j

Next i

End

Sub 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 i

End Sub