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Both melons and cucumbers grow quickly from pips if started off in spring in the same way as citrus pips (see in this fruit gorwing section), but with warmth throughout their life. Small plants should have grown within a month or two, with 4 foot creepers by the end of the year.
These will need strings or wires fixed to a wall to which to cling. You may even get edible fruits if you cross-pollinate the flowers of each plant, by dabbing them with cotton-wool.