Why do this problem?
This investigation offers an opportunity for children to work creatively, as there is no obvious place to start. However, it may well give you chance to discuss systematic approaches once they have been working on it for a while.
You'll probably get the best discussion and thoughts from the pupils if you 'act' out the situation. You are the ice cream vendor with a selection of cards, counters, cubes etc. to represent the ice cream. Make sure that the class can see the choices that the previous pupil(s) made and encourage them to check if they've kept to the rule, helping as little as possible.
Once they have got the idea, invite them to work on the problem, perhaps in pairs. Allow them to make their own decisions as to the equipment they use and the way they record - sharing these can be just as valuable as sharing solutions.
This activity would lend itself to a display and so you may want children to work on large sheets of paper which could be the stimulus for a plenary and could then be put straight up on the classroom walls. You could invite some children to explain how they have found different ways of seven children having ice cream. Draw attention to those who have found a systematic way of finding
Why did you choose that flavour?
Is there a way of choosing to let more pupils have a choice?
As the problem suggests, the thinking can be extended by looking at larger numbers of flavours.
For more extension work
From the "Possible Extension" the challenge would be to find a general formulae that would take into account the number of flavours and how many scoops were alloed each time to produce the largest numbers of hungry ice cream addicts who could have their fill. Then there would be the need to prrove it to be correct.
This problem is a good context in which to try to stand back and encourage pupils to support each other and explain ideas themselves. Working in pairs might be an appropriate way to support this.