/LMAR=0/XLINE=3/FONT#0=BAXL30/FONT#1=BAXM30/FONT#2=BAXB30/FONT#3=SUB/FONT#4=SUP/FONT#5=BASL35/FONT#6=NGR25/FONT#7=MATH30/FONT#8=FIX25/FONT#9=GRK30



␈↓ ↓H␈↓α␈↓ ¬λReasoning about Knowledge

␈↓ ↓H␈↓␈↓ α_The␈α
following␈α
problem␈α
is␈αmuch␈α
more␈α
difficult␈α
to␈α
formalize␈αthan␈α
the␈α
␈↓↓Wise␈α
man␈α
problem␈↓␈αor
␈↓ ↓H␈↓the ␈↓↓Unfaithful wives problem␈↓:

␈↓ ↓H␈↓␈↓ α_Two integers, 1 < m, n < 100 are chosen.

␈↓ ↓H␈↓␈↓ α_Mr␈α
P.␈α
and␈α
Mr.␈α∞S␈α
are␈α
two␈α
mathematicians.␈α∞ Mr.␈α
P␈α
is␈α
given␈α∞the␈α
product␈α
of␈α
the␈α∞two␈α
chosen
␈↓ ↓H␈↓integers, and Mr. S. is given the sum.  Both of these gentlemen are perfectly logical.

␈↓ ↓H␈↓␈↓ α_They␈αare␈αasked␈αwhat␈αm␈αand␈αn␈αare.␈α Obviously,␈αif␈αMr.␈αP␈αknew␈αthe␈αsum,␈αor␈αMr.␈αS␈αknew␈αthe
␈↓ ↓H␈↓product, they could figure out the values of m and n.

␈↓ ↓H␈↓␈↓ α_Here are their answers:

␈↓ ↓H␈↓␈↓ α_P says: ␈↓↓I don't know.␈↓

␈↓ ↓H␈↓␈↓ α_S says: ␈↓↓I knew you did't know.  Neither do I.␈↓

␈↓ ↓H␈↓␈↓ α_P says: ␈↓↓Oh! Now I know.␈↓

␈↓ ↓H␈↓␈↓ α_S says: ␈↓↓Same here.␈↓

␈↓ ↓H␈↓␈↓ α_Find the values of m and n.