The puzzle is as follows:

The figure from below represents a peculiar structure which consists in congruent triangles whose sides intersect and is made of an iron wire. How many cuts passing through all the dots showcased can be made at minimum to get the whole structure unassembled? Assume that a cut through any of the edges or vertex it can separate the wires passing through that vertex. Also assume that it is allowed to move the pieces from its original position after the dissection has been made. Also assume that folding of this structure is not allowed.

Sketch of the problem

The choices given are:

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

This dissection puzzle is more complicated. I've attempted several ways to dissemble the structure but I get more cuts than what it is offered in the choices. Where could those cuts be made?

I think there's an implicit clue that the intended approach does now allow bending the structure. Hence only allowing cutting by diagonals.

I've attempted all sorts of ways for more than an hour or so. Thus I am requesting help, and I would appreciate a diagram for where to make cuts. Is there any general guideline for how to solve this type of problem?

For reference I found this in a collection of Puzzles challenges. From the looks of it seems to be an adaptation from an APA IQ exam of the late 1970s or mid 1980s from an older Leon Thurstone or Wechsler exams of intelligence.

  • 2
    $\begingroup$ There is a lot of ambiguity here. For example, are we allowed to move pieces after each cut? Does it matter if we cut through edges? $\endgroup$ – hexomino Mar 3 at 11:29
  • $\begingroup$ Furthermore, rot13(fnl V phg guvf va unys jvgu bar phg. Gura cynprq bar unys ba gur bgure unys. Qbrf phggvat guebhtu 2 ynlref ng bapr pbhag nf bar phg be 2 phgf?) Because that seems to be the ticket to the least cuts. $\endgroup$ – MacGyver88 Mar 3 at 16:17
  • $\begingroup$ @hexomino Sorry about that, I included new clue which it was not mentioned in the beginning maybe now can it be reopened?. This clears the situation as I feel maybe this caused some initial confusion. $\endgroup$ – Chris Steinbeck Bell Mar 4 at 3:18

You could solve it using

6 cuts

As following:

enter image description here

  • 1
    $\begingroup$ You could probably save a few by layering the wires over each other after the first few cust. At minimum, you could save two - make three cuts, leaving you with six identical pieces, and then layer them all on top of one another for one final cut. $\endgroup$ – Ben Barden Mar 3 at 15:13
  • $\begingroup$ @BenBarden True. Without moving the pieces though, I think that is the most concise solution. $\endgroup$ – Joe Kerr Mar 3 at 15:33

I considered that:

  1. The cuts are straight;
  2. I'm able to cut multiple wires at the same time;

So considering the basic shape, I first cut it in half (since it's symetrical let's assume I cut it following a horizontal line), I obtain this shape:

after the first cut

Now I superpose the two figures and cut them in half again:

after the second cut

Now I reckon that two more cuts are necessary. So only 4 cuts.

But maybe somebody can figure out a way yo do it in three!

  • $\begingroup$ folds are not cuts, though. It has to be fully sliced even after you unfold it. $\endgroup$ – Ben Barden Mar 3 at 15:10
  • $\begingroup$ I edited the hypothesis since I never bend the shape. In fact, when I cut it superpose the similar shape as to slice more dots. $\endgroup$ – kronenbouh Mar 3 at 15:32
  • $\begingroup$ Ah. I get it now. I think 4 may be the limit without folding. With folding... well, technically, ti should be possible to fold it enough to get all of the original 6 cuts from the nonmoving version to line up with one another at which point it's only one cut. As such, I think that folding is not permitted, and that 4 is optimal. $\endgroup$ – Ben Barden Mar 3 at 19:16
  • $\begingroup$ @kronenbouh Welcome to Puzzling SE! I'm the OP of this question. First sorry for the late reply. I originally edited the question to add more clues including that the structure can be moved from its position once the dissection has been made. It seems that you included this strategy in your solution. But have you also considered that some cuts can be made on any vertex to reduce their number?. I have no idea if this dissection can be made in less. Can you please attend this doubt of mine?. $\endgroup$ – Chris Steinbeck Bell Mar 8 at 21:51
  • $\begingroup$ Hello, I cannot find a way to do it in 3 cuts, so I maintain my initial answer :) $\endgroup$ – kronenbouh Mar 18 at 7:55

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