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A day ahead, divide the pomegranate seeds between the holes in an ice cube tray, top up with water and freeze.
Reserve half the mint for serving, and tear the rest into a large jug with the lime quarters. Using a rolling pin, bash the mint and lime to release the flavours. Add the pomegranate juice and lemonade. Put ice cubes in each glass, then strain over the pomegranate mix through a small sieve. Garnish with lime slices and more mint.