e no ambiguity in the notation.

[Illustration]

The diagram may be simplified by my "buttons and string" method, fully
explained in _A. in M._, p. 230. It then takes one of the simple forms of
A or B, and the solution is much easier. In A we use counters; in B we
can employ rooks on a corner of a chessboard. In both cases we have to
get the order

[Illustration:

{1 2 3}
{4 5 6}
{7 8 } ]

in the fewest possible moves.

See also solution to No. 94.

14.--_The Weaver's Puzzle._

The illustration shows clearly how the Weaver cut his square of beautiful
cloth into four pieces of exactly the same size and shape, so that each
piece contained an embroidered lion and castle unmutilated in any way.

[Illustration]

15.--_The Cook's Puzzle._

There were four portions of warden pie and four portions of venison pasty
to be distributed among eight out of eleven guests. But five out of the
eleven will only eat the pie, four will only eat the pasty, and two are
willing to eat of either. Any possible combination must fall into one of
the following groups. (i.) Where the warden pie is distributed entirely
among the five first mentioned; (ii.) where only one of the accommodating
pair is given pie; (iii.) where the other of the pair is given pie; (iv.)
where both of the pair are given pie. The numbers of combinations are:
(i.) = 75, (ii.) = 50, (iii.) = 10, (iv.) = 10--making in all 145 ways of
selecting the eight participants. A great many people will give the
answer as 185, by overlooking the fact that in forty cases in class
(iii.) precisely the same eight guests would be sharing the meal as in
class (ii.), though the accommodating pair would be eating differently of
the two dishes. This is the point that upset the calculations of the
company.

16.--_The Sompnour's Puzzle._

The number that the Sompnour confided to the Wife of Bath was
twenty-nine, and she was told to begin her count at the Doctor of Physic,
who will be seen in the illustration standing the second on her right.
The first count of twenty-nine falls on the Shipman, who steps out of the
ring. The second count falls on the Doctor, who next steps out. The
remaining three counts fall respectively on the Cook, the Sompnour, and
the Miller. The ladies would, therefore, have been left in possession had
it not been for the unfortunate error of the good Wife. Any multiple of
2,520 added to 29 would also have served the same purpose,