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Is it possible to glue up the tiles without removing them?

There is a heated floor in the kitchen, covered with tiles 50/50 cm. Good Italian tiles, not a single crack, lying on the floor for about 20 years. The trouble is that many of the tiles peeled off at its area, while standing firmly in place due to the grout that almost anywhere did not fall off. When you walk on these tiles, there is an unpleasant creaking sound. Since the tiles are good, completely remove and replace all I do not want to.

Are there options to pour under them some kind of liquid adhesive, without removing the tile?

• tiles
• heated floor