I have created the following simple tiling puzzle for children.

The puzzle consists of 9 tiles shown below (4 pieces of type A, 4 pieces of type B and 1 piece of type C):

enter image description here

The goal of the puzzle is to arrange the 9 tiles to form a 3x3 square such that the border of the square is all blue. You are allowed to rotate the tiles.

The solution is:

enter image description here

My question is what age group is this puzzle appropriate for (not too easy, not too tough)?

  • 3
    $\begingroup$ I'd guess 4 to 10 years old, but that's just a guess. $\endgroup$
    – Sue VanHattum
    Commented Nov 25, 2023 at 22:36
  • 6
    $\begingroup$ I'm afraid that the transition from "too hard" to "too easy" in terms of age is very abrupt here, so there is no noticeable "appropriate age span" whatsoever. As soon as the child is capable of understanding that the negation of "the whole border is blue" is "there is a red at the border", i.e., doesn't try to complete a picture that is already hopeless, it becomes trivial. Before that had been realized the number of possibilities is rather big. I don't know when this transition happens, but I would certainly find it a "non-puzzle" when 6 years old, quite possibly 5. $\endgroup$
    – fedja
    Commented Nov 25, 2023 at 23:31
  • 2
    $\begingroup$ Your question is incomplete: are you just showing the images of those tiles or are you actually giving such tiles to the children? In top of that, here in the question you have mentioned the amount of tiles for every type. What if you don't mention that and you clearly indicate that all kinds of tiles must be used and the solution must be rotation-independent (when you turn it 90°, you must still have the same solution) $\endgroup$
    – Dominique
    Commented Nov 26, 2023 at 10:01
  • 2
    $\begingroup$ I would guess be anywhere from $5$ - $14$ years old. I would expect a "smart" $7$-year old to get it, and I wouldn't be surprised if a struggling $14$ year old doesn't get it (due to comprehension issues or lack of mathematical experience). $\endgroup$ Commented Nov 26, 2023 at 12:05
  • 1
    $\begingroup$ @Dominique I would be giving the children the actual physical tiles. Your rotational variant is interesting. $\endgroup$ Commented Nov 26, 2023 at 19:26

1 Answer 1


I'd say it depends highly on how it's presented. "What's the prettiest picture you can make with these nine tiles?" will probably go with any age. "Bad" solutions can then be elaborated on by "But what if ..."s. Why not initially test it on a sample of different ages in this form, and evaluate how it's handled by different ages?

  • 3
    $\begingroup$ "What's the prettiest picture you can make with these nine tiles?" That reminds me of the (in)famous series of pictures about the progress of the math education in the USA that starts with "find the area of <some domain bounded by lines and circular arcs>" and ends with "color the given rectangle with your favorite color". But +1 for trying to save the puzzle :-) $\endgroup$
    – fedja
    Commented Nov 27, 2023 at 23:12

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