Question

Three Bears

In the land of Plentiful Honey, lived three bears: Papa
Bear, Mama Bear and Baby Bear. They had three pots
of honey: one large, one medium, and one small. One
day they found themselves carrying the pots of honey
down a path. Papa was carrying the medium pot, while
Mama was carrying the small pot, and Baby was
carrying the large pot. This was clearly inequitable and they decided to trade pots, so that
each was proportional to the size of the bear. It may seem there is a simple solution to their
dilemma, however, the rules for transferring pots in the land of Plentiful Honey are quite
complicated. They are:
a) Only one pot of honey can be passed at a time.
b) fa bear is holding two pots of honey, only the smaller pot may be transferred.
• A honey pot may not be transferred to a bear that is holding a smaller pot.
d) Pots may not be set on anything, such as the ground or a stump.
Diagram or explain the sequence of the transferring of honey pots, so that Papa Bear has the
large pot, Mama Bear the medium pot, and Baby Bear the small pot.

Answer 1

m→B, s→P, m→M, s→M, l→P, s→B

Explanation:

The initial state is ...

(Baby, Mama, Papa) = (Large, Small, Medium)

The large pot can only be transferred from someone holding only that pot, and only to someone holding no pots. The small pot can go anywhere any time.

Transfer the medium pot to Baby.

(B, M, P) = ({L, M}, S, –)

Transfer the small pot to Papa.

(B, M, P} = ({L, M} –, S)

Transfer the medium pot to Mama.

(B, M, P) = (L, M, S)

Transfer the small pot to Mama.

(B, M, P) = (L, {M, S}, –)

Transfer the large pot to Papa.

(B, M, P) = (–, {M, S}, L)

Transfer the small pot to Baby.

(B, M, P) = (S, M, L) . . . . . . desired end condition