I think different people want different things. Looking at the comments it seems that a lot of people are keen to write the most elegant or the shortest code they can. For me the point is to come up with the code that gives the correct answer (within the program run time constraint) in the shortest possible time spent working on it. In other words if I can reduce the solution time from 59 seconds to 1 microsecond with less than 58 seconds worth of coding, that’s worth doing, otherwise it isn’t and I’ll move onto something else. The only proviso is that if the code is re-useable (either in Project Euler or elsewhere) then it’s worth spending some time optimising it.

…mrt

Email on it’s way from my work address. dbb may be right.

…mrt (Happy New Year to all!)

A recursive approach can be easily generalized to search for a target T with N possible ‘buckets’ whereas a nested loops approach requires a code change whenever N changes. For example, how many ways can you come up with $250 using bills / coins of denomination 100, 50, 20, 10, 5, 2, 1, 50c, 25, 10, 5, and 1? With a recursive approach, only the input data set would change.

The recursive code for 31 should be easily adaptable to 76! Just use 99 buckets, 1, 2, …, 99. The big difference is that we must use at least 2 buckets in 76 whereas in 31 a single bucket is acceptable.

It should not be very difficult to generalize the VBA code at
Find a set of amounts that match a target value
http://www.tushar-mehta.com/excel/templates/match_values/index.html

The only difference between the code on that page and the requirement for 31 is that the code imposes an implicit restriction that each bucket (value) be used only once. For 31 each value can be used as often as required. But, that should be a trivial change to the code. I’ll try it tomorrow and share the results. Adapting the code for 31 to 76 will require some additional work. But that too should not be too difficult. Hopefully, I will not have to eat my claim that the recursive approach requires a trivial change. {grin}

Here is my full code with a text substitute for the “less than” sign

Sub P76()

Dim m As Long
Dim t As Single
t = Timer
fP76 100, 0, m
Debug.Print m – 1, (Timer – t) / 60

End Sub

Sub fP76(ByVal n As Long, ByVal S As Long, ByRef m As Long)
Dim i As Long
Dim t As Long
For i = n To 1 Step -1
t = S + i
If S = 0 Then Debug.Print i; m
Select Case t
Case Is LESSTHAN 100
fP76 i, t, m
Case 100
m = m + 1
End Select
Next i
End Sub