From the Common Sense Problem Page


The Surprise Birthday Present

Alice and Bob want to surprise their sister Carol with a joint present for her birthday, two weeks from now. They therefore go into a closed room to decide on the present and to plan how they will buy it.

The plan will not work:

  • If Carol is also in the room.
  • If the door is open and Carol is in the next room.
  • If one of them tells Carol.
  • If they do not consult together.
  • If they can't agree on a present.
  • If they wait until after Carol's birthday.
  • It will probably not work if Carol sees that they have the present before they give it to her.
  • On the other hand, it probably will work if Carol sees the present in the store.
  • The plan will work if, instead,
    • They discuss the plan during a walk outside.
    • They pass a hidden written message.
    • They go together to buy the present, or one of them goes singly to buy the present.
  • Non-prediction problems:
    • If Carol is not surprised, infer that she somehow got wind of their plan.
    • If the plan is executed, and we know that Alice has not spent any money, then infer that Bob bought the present and that Alice owes him for her share.
    • If Alice and Bob present Carol with present P on her birthday, infer that P is the present they decided on.
The following constraints must be satisfied by the solution:
  • The events enumerated in this plan are not the only events that will transpire in the next two weeks, or even the only actions of Alice and Bob in the next two weeks. Therefore, it will be considered a weakness in a theory if it supports, either monotonically or non-monotonically, the inference that nothing else happens.
  • Similarly, Carol knows lots of stuff; she just doesn't know about the present. It will be considered a weakness in a theory if it supports the inference that Carol knows nothing at all (or, more precisely, that she knows nothing except truths that hold in all possible worlds).
Note that the problem involves a variety of domains: time, a little space and physics, knowledge, perception, naive psychology, multi-agents.

Contributed by Ernie Davis (, New York University, U.S.A. (29th May 2001)

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