# I’m bored

Discussion in 'Math' started by Hymie, Aug 12, 2018.

1. ### Hymie Thread Starter Active Member

Mar 30, 2018
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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.

2. ### oz93666 Senior Member

Sep 7, 2010
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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

Last edited: Aug 13, 2018
3. ### panic mode Senior Member

Oct 10, 2011
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define "single cut".
does that include "Z" cut that separates board into 4 pieces?

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4. ### Ian Rogers Active Member

Dec 12, 2012
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Not really a "single cut"
3 steps of 0.4 long and 0.3 high

Last edited: Aug 19, 2018
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5. ### oz93666 Senior Member

Sep 7, 2010
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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

6. ### panic mode Senior Member

Oct 10, 2011
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ok, it does mention "two pieces" only

7. ### oz93666 Senior Member

Sep 7, 2010
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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

8. ### cmartinez AAC Fanatic!

Jan 17, 2007
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... 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?

9. ### Hymie Thread Starter Active Member

Mar 30, 2018
504
109
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.

Apr 30, 2011
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Last edited: Aug 13, 2018
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11. ### jpanhalt Expert

Jan 18, 2008
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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.

Mar 30, 2018
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13. ### MrChips Moderator

Oct 2, 2009
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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.

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14. ### jpanhalt Expert

Jan 18, 2008
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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.

15. ### Hymie Thread Starter Active Member

Mar 30, 2018
504
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For those who have not visualised the solution I offer the attached diagram which shows the single cut as the solid red line.

16. ### MrAl AAC Fanatic!

Jun 17, 2014
5,176
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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.

17. ### MrAl AAC Fanatic!

Jun 17, 2014
5,176
1,119
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.

Mar 30, 2018
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19. ### WBahn Moderator

Mar 31, 2012
22,980
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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.

20. ### ConstructionK88 Member

Jul 25, 2018
148
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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.