THE CANTERBURY PUZZLES
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102.A Reversible
Magic Square.
It will be seen that in
the arrangement given
every number is different,
and all the columns, all
the rows, and each of
the two diagonals, add
up 179, whether you
turn the page upside
down or not. The reader
will notice that I have
not used the figures 3,
4, 5, 8 or 0.
103.The Tube Railway.
There are 640 different routes. A general formula for puzzles of
this kind is not practicable. We have obviously only to consider the
variations of route between B and E. Here there are nine sections
or " lines," but it is impossible for a train, under the conditions, to
traverse more than seven of these lines in any route. In the follow-
ing table by " directions " is meant the order of stations irrespective
of " routes." Thus, the " direction," B C D E gives nine " routes,"
because there are three ways of getting from B to C, and three ways
of getting from D to E. But the " direction " B D C E admits of
no variation ; therefore yields only one route.
2 two-line directions
1 three-line
i
2 four-line
2 .,
6 five-line
,
>
»
>
»
of 3 routes
i ,.
,. 9
6
18
6
Carried forward
1
6
1
9
12
36
36
100
