Forgive me Wahaj. I hadn`t realised that everything had become quite so...detached. However, try to visualise your pre-detachment dahlia as looking like your cosmos, with the tubers (albeit somewhat plumper) all joined to the stalk in a similar fashion. Around the very base of the stalk where the tubers join it is a slight collar (there`s a similar one on your cosmos) and around that collar were a number of eyes. For normal propagation the complete bunch of stalk and tubers (again looking like your cosmos) is started off as a single entity in the spring and the shoots which spring from the eyes are taken as cuttings.
Where the tubers are divided up this also is normally done in the spring. The complete plant is started into growth and is not divided until the first eyes have started to grow out as shoots. Most of the shoots are from the old collar, but some arise from the top part of the tubers themselves. Only then can it be seen which tubers have viable eyes, and the stem and tubers are then carefully divided up to leave one growing eye on each part.
From your picture it looks as though the stalk ends of the tubers are the ones pointing to the bottom of the picture. Look at these carefully at these to see whether you can see any sign of a dormant bud, but you probably won`t. I`m afraid that with such complete separation your only hope is to store the individual tubers and in spring set them out in compost with only the root ends covered, keep them warm and moist and see whether any shoots arise. Several of the individual tubers look reasonable so you`re in with a chance.
