# Least cuts to get 44 rods from a metal grid

The puzzle is as follows:

Suppose that you have a metal structure made by brass wire. Assuming that you must get 44 rods of the same size each. What is the least cuts to be made using an electric grinder assuming that you cannot bend the structure?

The choices given are:

1. 5
2. 6
3. 4
4. 7

I have been going in circles on how to arrange this figure to get the least amount of cuts. My understanding is that a in typical puzzle of this type, cutting diagonally is useful to put the pieces adjacent to each other. This allows you to not repeat the cut twice.

My problem arises from the little square in the center. It confuses me. I can see that the structure is symmetric. Does this help to minimize the number of cuts?

Is this logic sound?

I've attempted to make a bigger X in the central square but then I got stuck from there.

I would really appreciate answers which include a drawing.

I found this puzzle in an old sheet of different dissection riddles. From its looks seem to be an adaptation from APA IQ exams of the 1980s which might be a modification from Catell's tests.

Can someone help me with this question?

• It is not clear to me what constitutes a cut. Is it a straight line through the whole structure? And if a cut goes through a vertex, do all four rods meeting at that vertex become detached from each other? – Jaap Scherphuis Mar 3 at 9:52
• My assumption was that a cut can divide two rods joined in an L, or three joined in a T, but can't divide 4 joined in an X. – Penguino Mar 4 at 2:12

If you don't need to use all the material and can rearrange material between cuts then you can construct at least 48 rods with only three cuts as shown below. So none of the optional answers appear to be correct.

Alternately, if you want to use all the material to make unit length rods, I believe it can be done in

5

cuts as shown in the following diagram.

Here is a slightly improved version of @Penguino's second interpretation of the puzzle, including the rule that four-way node are not fully split by a single cut but first split into 1-1-2, even though I do not understand where that comes from. Following a suggestion by @BenBarden it is assumed that the two singles must lie on the same side of the cut.

• The form you have presented would be a very strange way for cuts 1&2 to work. I think the idea is that you have to decide which side of the 4-way corner to err on (slightly) rather than going straight down the middle. – Ben Barden Mar 9 at 18:06
• Fortunately, it doesn't break your solution, as the resulting shapes can still overlap just fin even if you break the center square differently. – Ben Barden Mar 9 at 18:10
• @BenBarden Better (see updated figure)? – Albert.Lang Mar 9 at 18:22
• Yup! I would have had them flipped, so that the wires all lined up, but that works fine. – Ben Barden Mar 9 at 19:26