Gem Maze opens at level 28 after you have spoken with Massy in the Quests.

After you have pressed the Accept Quest for Gem maze, it will appear in the right hand side accepted quests (Highlighted)

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Press the Open Gem Maze Interface.
This will Open the Gem Maze Window

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You now have 10 moves, make one move at a time to make a minimum of 3 of the same colour Gems in a line to get rewards.
The more you can get in a line the greater the rewards you will receive. This also works with one move getting multiple rewards

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As you can see by the picture above. by swapping the Blue and Green gems will activate two times three Gems at once. This will give you greater rewards.
Once you have exhausted your 10 goes, the rewards you have achieved can be seen in the Today's Rewards Panel.

You can get an extra 10 goes by pressing the Buy Energy button under the Gems window.
The price for these extra goes is 30 gold per 10 extra Energy.

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When you have reached enough points through your Gem conversion, a chest will become available to you. The greater the points you have amassed, the more chests will open for you.

The amount of points that each chest requires is as follows:

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There is a final 5000 point chest.

Once you have achieved the required amount of points you can claim the rewards.

When you attain the required level, more free attempts are made available to you.

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Each new level will be opened at the following:

28 Basic
36 Promoted
41 Advanced
46 Master

These levels can also be increased by purchasing extra Energy.

Take your fill of Gems, and enjoy the game as much as I do. (Happy Gaming)