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How Knot To Hang A Painting

Tom Scott | January 26, 2026



Subscribe to Up and Atom! https://www.youtube.com/channel/UCSIvk78tK2TiviLQn4fSHaw/ or start with Jade’s video on quantum tunnelling: https://www.youtube.com/watch?v=WPZLRtyvEqo

You’ve got a painting and two nails. Can you use both nails to hang the painting so that if either nail is removed, the painting falls? That’s the puzzle: in this week’s guest video, Jade’s going to solve it with maths.

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Written by Tom Scott

Comments

This post currently has 48 comments.

  3. @mateuscrevelin3394

    January 26, 2026 at 5:51 pm

    I watched this video when it came out. Remembered it a couple days back randomly and wanted to watch it again. Proceeded to spend two hours searching it among Up and Atom's videos and give up. Had YT recommend it to me just now and noticed its a Tom Scott video… 🙁

  6. @ilannlabbe9321

    January 26, 2026 at 5:51 pm

    Please tell me I wasn’t the only one to think of just putting the two ends around one pin and then at the 2 places in the middle of the string where it “folds”, collect those and rotate them to put them around pin 2

    I just thought it through looking at bends in the string rather then crossings. A similar concept to that of the video applies: if I want the string to come off pin A when removing B, I need two folds in the string to go around A; one to hold on, and another which can cancel it. Now the rest of the string needs to be secured at pin B, which we can do with exactly the same method, since we are left with two string bends…

    You can just think of it as a circle folded in half:
    If an ‘O’ becomes a two layered C, the “ends” of the C is where the string “turns around”. If you bring those two ends together you get

  7. @DustInCompDev

    January 26, 2026 at 5:51 pm

    I know this is 6 years late, but I'm somehow not seeing a single comment point out how at 7:47, on the right side, the strings that are supposed to slide counter-clockwise around the green pin just slip over it instead.

  13. @halwiseman2625

    January 26, 2026 at 5:51 pm

    Use two strings. On one string hang the picture. Loop that string over the other and hang string 2 over the pins such that string 1 is hanging from the middle of string 2. Pull a pin and down will come picture and string 1. String 2 will be left hanging on the remaining pin.

  20. @mehere8038

    January 26, 2026 at 5:51 pm

    Interesting, although not actually needed for this particular puzzle. I stopped before the video stop point & thought about it & realised you could easily do it simply with no knots at all, wrap the string around the pin a few times & then push it into the wall hard & it will hold the string in place (unless the pin is removed), then run the string through the picture hole, then back up & over the pin, over to the second pin, over it, down around the picture hole, then back up to the pin & wrap around a few times & tighten the pin into the wall.

    All holds perfectly unless either pin is removed, in which case the string slides out of both painting holes & ends up hanging straight down just by whatever pin is left.

  22. @fefesfrtwet

    January 26, 2026 at 5:51 pm

    Pass the string through the holes in the painting (I'm going by the image). Pierce either end of the string with the pins (or if this is not possible create a knot smaller than the diameter of the holes) and then attach to the wall. Either pin being removed allows the string to pass through the holes.

  31. @xzysyndrome

    January 26, 2026 at 5:51 pm

    Classic example of overthinking simple solutions. I pushed 4 thumbtacks into my signed Salvador Dali print so I could see it everyday. My buddy lost his mind….I didn't understand his stress.

    "Do you know what that is worth?"
    Nope…not selling it…don't even care.

  36. @ano_nym

    January 26, 2026 at 5:51 pm

    I don't really get the notation with the drawings.
    5:49
    Here we can clearly see 1 going over 2, so it's x, but then we see 1 going under 2, and it's still x. Same with 2 going over 3, y, then 2 going under 3, but is still y. Why aren't they -1 there at the second ones?

  43. @chrishei3111

    January 26, 2026 at 5:51 pm

    this video is terrible. it didn't revisit the original problem enough, it was just a poor crash course in knot theory. there's so many intuitive answers, just use the pins on either end of the string and don't make a loop out of the string. Not to mention hanging a picture like this looks horrible, its not even a good question to answer. Get a nail and hammer. That's the actual answer.

  46. @tommiller1315

    January 26, 2026 at 5:51 pm

    Being lazy, I paused the video at the before point, ignored the maths, and just came up with the solution as shown, in my mind.
    Decades ago, I did Edward de Bono's 7 day course on lateral thinking the same way in under an hour. (The one with milk bottles and knives).

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