A recent Torah Minute,
Reassembling an item on Shabbath generated a lot of questions. A question uppermost in many people's minds was whether it is permitted for children to play with Lego and jigsaw puzzles on Shabbath.
There are many authorities who permit children to play with Lego on Shabbath, and part of the reasoning is that the whole purpose of Lego is that is not permanent and is meant to be taken apart. Therefore, it is not considered to be the forbidden Shabbath act of building (Boneh).
There are different opinions among Posqim about puzzles on Shabbath. Some authorities permit children to play with them if they are not made in a frame. Others believe that it may come under the category of writing on Shabbath and forbid it.
The Ohr Lesion states that young girls may play with Lego, but that boys should not be given Lego to play with, since this will get them used to Bittul Torah (playing instead studying Torah). Adults, he adds, are forbidden even to touch it. As far as puzzles are concerned, he states that young girls may play with them even if they are in a frame and that "writing" does not apply. However, he states that boys should not play with them for the reason outlined above.
(See Ohr Lesion
2-52:6, Shemirath Shabbath Kehilkhatha 16: 18, Yehawweh Da'ath Beh, Siman Nun Heh)
