Math Puzzler: Can You Make A Rectangle With One Cut?

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[cshotton]

There is an easier solution depending on the actual dimensions. Just cut vertically along the inner edge of one of the tabs and rotate the resulting piece 90 degrees and insert in the appropriate place. The video solution is technically multiple cuts and implies that the only solution is to make symmetric pieces. If the dimensions allow, it's easier just to trim off one end and fill in the empty space with the trimmed rectangle.

[MindYourDecisions]

Thanks all. In hindsight I should have added dimensions and also solicited additional solutions.

[Foxintox]

I'm pretty sure you can cut vertically, along the inner edge of the "tab" and place that vertical piece horizontally next to the other tab.

[中野優作-bn]

You can also just cut it horizontally in the middle, so itll look like two leaning "L"s, then u can make a rectangle

[ScottMillerWhiteMorning]

I see a second solution. Cut it straight down from where one of the tabs protrudes so it makes a 3x1 piece. That piece will fit right next to the other tab.

[MindYourDecisions]

Thanks to Boing Boing for sharing this video.

Yes, I overlooked alternate solutions. Here are three illustrations of solutions people have kindly shared over Twitter.

[edancoll]

We were supposed to assume that the tabs' sides are exactly half the length of the rectangle's sides? If so, I could have assumed infinitely many things for infinitely many solutions.

[Sergio_Loureiro]

I didn't even consider this, because I tought that were 3 cuts.

[Qermaq]

Thinking further... assume the tabs are rectangles with height th and width tw, and the remaining small rectangle has h and w, if th=h/i where i is NOT an integer you can’t do it so easily. Consider tabs 2x2 on a rectangle with h 3 and w 7.

[jeffreydonadio]

You said to cut the shape into two pieces by making only one cut, yet your solution relied on making three cuts, not just one. When you said "only one cut", that implied drawing one straight line, and then cutting the shape once along that line. I wish that you would define the rules better before you play the game. Your terminology leaves a lot of room for error.

[MateoJH]

I interpreted "one cut" as being a straight line, and would have cut horizontally along the middle. They would then fit together just like two L-shaped Tetris pieces to form a rectangle.

[XCyclonusX]

a zig zag is three cuts. One cut horizontally down the middle. You'll have two L shapes that can be brought together to form a rectangle.

[davem.]

You can also cut right across horizontally and fit the two parts together to form one long rectangle.

[joshualiley]

Horizontally down the middle, to form a long rectangle, or diagonally, from where you started the staircase to where you ended, or cut vertically down from one of the tabs

[theexcruciator]

I thought that the cut lines had to be straight. This wasn't clarified in the video.

[MathFun_by_ManuelGarcia]

If you take the piece in the right corner not just the small square but the whole portion from the top to the botton, it forms a rectangle that perfectly fits (horizontaly) at the right of the left corner's small square

[cameronlambert]

Let’s just agree there are a ton of correct answers for this

[DaveScottAggie]

I did a horizontal line through the middle. Move the bottom portion to be above the other portion, just to the left of the tab. Now you have a rectangle which is 2 units tall and 6 units wide.

[joshualiley]

Considering we didn't know the dimensions, we were just assuming that the tabs fitted perfectly with half the larger rectangle. But now we know this, we could also cut the shape in half, from left to right, or cut one tab off and put it next to the other tab

[flatman]

You can do it with a single straight cut just cut vertically in x=1/5 of the maximum horizontal lenght (L) of the initial shape then the smaller piece is a rectangle of 1/5L X 3/5L which fits on top of the other piece to form a rectangle of 4/5L X 3/5L