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I once played a game in which players need to make a chain of plastic rectangular blocks by hooking them together. The plastic blocks are coloured and semitransparent. First block hooks to the top of a tower and player continues attaching blocks.

A player would lose the game if the tower topples due to heavy weight of chain. Player can start as many chains as they like from the tower by adding a new piece at top of tower as long as there's space available.

Note: The name of the game includes Jenga word in it but I'm unable to recall the entire name. I have drawn a sketch of how the game looks like. sketch of game

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This appears to be Jenga Max. Here's the description from the overview on Board Game Geek:

Jenga Max is a dexterity game similar to but different from Jenga. Players take turns attaching plastic pieces to the top of a tower. There are different ways of attaching pieces together, and if an added piece disturbs the balance of the tower, it will fall down and the player loses. The winner is the last play who successfully placed a playing piece.

The back of the Jenga Match box with an illustration that matches the original post author's illustration

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