A man had a room with only one window in it.  It was a square window, 1 metre high and 1 metre wide (see diagram).  Unfortunately, the man had sensitive eyes and the window let in too much light. The man sent for a builder, and told him to alter the window so that it let in half the amount of light.  To make the matter especially tricky, the man insisted that the resulting window also had to be square, and 1 metre high and 1 metre wide.  The builder isn’t allowed to use curtains, or shutters, or coloured glass. How did the builder solve the problem?

As ever, please do NOT post your answers, but do say if you think you have solved the puzzle and how long it took. Solution on Monday.

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for theKindle (UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.


    1. Yup. Same here. Although, I’m less impressed at solving it so quickly and more impressed by how it’s a nice twist on an old puzzle.

      I kept thinking to myself as I read it “Wait, don’t I know this one. It sounds just like X”, and when I got to the edn I was right.

  1. I think I got a sollution, but I’m not sure it garantees 50% of light yet. Have to calculate for it, but do not have time to do so now.

    1. Ahh I see what you are getting at. Maybe instal the window on the floor ensuring that half of it sticks outside and half is covering the floorboards.

    1. Why not install a flagpole right out side the window and hang the material on it. That will block out the light>

  2. I can see the answer RW is angling for, but would question whether the problem is fairly stated.
    Also the question is ambiguous – are the “meters” gas meters, electric meters or some other type of measurement device?

  3. I think I’ve got a solution but, like -M-, I don’t know exactly the right numbers. Looking at other comments, some people have different answers. Monday will be interesting.

  4. I’ve been in the double-glazing industry most of my working life and I’ve never before encountered this situation

  5. As always some deliberately vague wording to generate discussion. By “high” and “wide” is Richard referring to the sides of the square or the diagonal measurements? If the original window was measured by the former method, then having it remade still square with the diagonals 1 metre across (ie diamond shaped) effectively results in half the area.

    Can we clarify this aspect?

    1. To me this looks like a simple request for clarification on Dave’s part rather than a spoiler. If the question was clearly worded Dave would not have asked for clarification; but then if the question was clearly worded there would be no puzzle – as this is basically a word puzzle more than anything else.

  6. I can think of multiple solutions for this one, however the one given away above (tsk tsk) has a certain “Richardness” if you excuse the neologism. So I suspect that we’re not talking about more major architectural changes or anything involving an above average understanding of the nature of electromagnetic radiation.

  7. I few seconds to think of an obvious answer, a few minutes with the aid of Mr. Pythagoras to confirm that my instinct was, indeed, a valid solution.

  8. I found the traditional answer and the tricky answer almost immediately, as long as the man didn’t need exact measurements.

    On the other hand, my very first workplace had a window next to my desk. Just outside the window was a 10 foot diameter column blocking out 95% of my view. So now I have three answers. One in the box, one near the box, and one ripping the box into shreds.

  9. Assuming that “curtains, or shutters, or coloured glass” essentially means “don’t put anything in front of the window?” Because there are plenty of other translucent materials one could place in the window besides curtains, shutters, or glass.

  10. Yes, definitely means don’t put anything in front of the window.
    I got the answer but it took me sadly long (2-3 minutes).
    I hope the guy is happy with the new amount of light coming in the window, as I don’t think you can do the trick again to get it down to a quarter of the light …

  11. I was thinking way outside of the box until i read the other statements made. I hope Richard chooses any of the stupid answers as the correct one! 😉

  12. The math here is greatly obscured by real-world issues. This is solvable only by looking at it obliquely. My brain refused to do that until I read the comments.

    1. ding! we have the winner. best solution yet (but we’ll need the Bad Astronomer to confirm the flux at that distance).

    2. Good idea for the puzzle, bad for the rest of us.

      The number is close enough. Taking 1 a.u. = 149.6 million km one would get 62 million km from a factor of 1 – sqrt(2), as direct consequence of the inverse square law.

    3. no need to move the earth. much hard to difficult to do. instead accelerate house into solar orbit at decent percentage of c [ c is same as speed of light in vacuum ]

      effect is that lengths forshorten. to us on earth will look like window is smaller. to rw in house, window will look same but sun will be smaller [ effect of Releativity ].

      thus puzzle solved.

  13. Like others, this one was a quick solution. Maybe because it’s a common puzzle that’s been presented in numerous forms over the years.

  14. This puzzle is attributed to Lewis Carroll, who wrote:-

    “”When I use a word,” Humpty Dumpty said, in rather a scornful tone, “it means just what I choose it to mean - neither more nor less.””

    RW has chosen a similar variable approach to the meaning of words in this puzzle using the same combination of words in two places to mean two different things.

    1. Was it Lewis Carroll who wrote “Alice in Wonderland” that featured the Queen of Hearts and the Jack of Squares?

  15. The customer sounds like a jerk… or some multinational mid-level manager. One answer immediately comes to mind, but I’m sure punching out one of his eyes isn’t the right answer.

  16. Whether or not it is *the* way the homeowner wants, I definitely have *one* way. And maybe the homeowner would like my idea!

    1. Water waves can be described as longitudinal waves, light as transverse waves. However in this case I didn’t use the wave model at all, I assume homogenous light rays orthogonal to the window-face.

      Thus an abstraction of the puzzle may be:
      In an xy-plane there is a square with a spread in x direction equals 1 meter and spread in y direction 1 meter and an area of 1 square meter. Find a square with the same spreads in x and y direction and area of 0.5 square meters.

  17. i used to think i was bright till i started coming here with all you lot of *easy peasy 30sec clever clogs*. but hurrah and rejoice! i ‘got’ this week’s in 2 min and i’m confident that i’m correct. then again i was confident with the toast one and look where that got me!

  18. About 30 secs to be sure I understood the problem with all its constraints, then about 20 secs to do the math to verify. Then I spent a bit of time figuring out how I would actually implement an aesthetic solution if I were the builder.

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