You have a piece of board measuring 1.6m by 0.9m. Your task is by using a single cut, cutting the board into two pieces - such that when the pieces are joined together they form a square board measuring 1.2m by 1.2m.
Dam ... I've spent to long on this already !!! I first thought of a staircase type cut .....one piece has to be flipped Now I think not necessary to have steps all the way .... the main cut must be 45 degrees but with step/s on the end
We must assume the cut is not straight , can go right up to the edge of the board and turn a sharp angle back to cutting again
Well spotted ... then I'm sure there must be a 45 degree cut ... going sleepy by now , if no one's cracked it when I wake up. I WILL spend some time and solve it
... I believe the statement about the single cut, but I'm not sure about the "only two pieces" requirement ... a possible approach for me would be to fold the board into a certain figure, and then perform the single cut, so as to obtain several pieces that will form the required square. Question, have you actually figured out a solution to the problem, or are you just teasing us?
To clarify things – the single cut of the board results in two separate pieces, when these two pieces are joined together they form a square 1.2m x 1.2m. Since the two areas (1.6m x 0.9m and 1.2m x 1.2m) are equal, no material is lost in the cut. The cut line may take any direction over the board, but results in only cutting the board into two pieces.
Dudeney's step dissection. Three steps, 0.3m X 0.4m. 0.9m + 0.3m = 1.2m & 1.6m – 0.4m = 1.2m https://demonstrations.wolfram.com/DudeneysStepDissectionOfARectangleToASquare/ I just noticed that Ian Rogers had it in post #4. Spoiler mask removed now since Hymie has revealed the solution.
The question about a zig-zag cut was raised, but not answered by Hymie. Most of Martin Gardner's tiling puzzles used zig-zag cuts. So long as the cuts are contiguous, changing direction does not constitute a separate cut in my view.
A "single cut" would generally be expected to mean a single straight cut. In order to make a zig-zag cut one would require a special tool such as a key-hole or jig saw.
Why not simply dispel the confusion: Is a zig-zag (e.g., staircase) allowed? As I mentioned, most of these tiling/geometry puzzles allow such cuts, and that is the only way I saw it being solved. It occurred to me that an arc cut might be considered a single cut (or a series of very small cuts that are contiguous), but I could not solve it with that either. BTW: I do not consider a scroll/coping saw a special tool.
For those who have not visualised the solution I offer the attached diagram which shows the single cut as the solid red line.
Hello, Is that the right solution? Something doesnt look right. Oh never mind, i thought you where flipping the right side board piece but now i see that it is just a translation shift: up 0.3m and left 0.4m after the cut.
Hello again, Hey the question comes up are there any other solutions? If not, is there a way to prove it? I would guess that everyone here has already seen the triangle folding into a square problem already, where you are allowed two folds. It's also an interesting geometrical way to view finding the area of a triangle with just one measurement.
Many puzzles like this rely heavily on ambiguous rules precisely because how most people will interpret them will preclude finding a solution. As long as a technically correct interpretation allows the solution, they are covered.
To speak in such a manner truly implies you would know the answer to the riddle with having to impose your oratorical skills upon us. Seriously dude. Speak dumb. We like that.