By studying solutions (and frankly looking for some trick), I have
discovered an “ugly” little truth that may or may not be well known (but
in the event it is not, I thought I would share it here).
Consider a 3-row block which consists of 27 little squares (within the
bold separators) – it happens that numbers travel together. What I mean
is that if, for example, the first 3 numbers across are 3 5 6, then you
can be sure that at least two of them will move across the 3-row block
together. That is, the 3 and the 5 OR the 3 and the 6 OR the 5 and
the 6 will appear in the same 3-square block in the rest of the section.
They may not be in the same order, or they have a separator between
them, but they will both be in the same little 3-square section across
those 27 squares.
In the puzzle I have just finished, the top 3 rows are as follows:
3 5 6 4 9 7 2 8 1
9 2 1 5 6 8 4 3 7
4 8 7 1 3 2 5 6 9
In this example, the 5 and 6 travel together and the 3,8, and 9 (their
neighbors in subsequent sections) are what I call “incidentals” and they
are incidental to the traveling pairs in the rest of the 27-square section.
If you look at the second row, you will see 9 2 1. If you already know
that 9 is an “incidental”, then you will know that 2 and 1 travel
together the rest of the way. Examination will also show that 4 and 7
go together in the same way.
The second and third sets of 3-row (27-square) blocks have the same
characteristics, but each of them has its own pairs and incidentals.
As to columns, the truth is still there but in this case, the overall
unit is a 27-square *column* AND the pairs are in a column as opposed to
being in a row. So as to columns in my example, it happens that the 9
and 4, the 5 and 2, and the 6 and 7 are the pairs, the new incidentals
being 3, 8, and 1. There is no correspondence (that I know of) as to
which are pairs or incidentals in adjacent 27-square rows or columns,
each being independent of its neighbors *and* no correspondence as to
which are incidentals in rows vs columns.
Obviously, you have to be pretty well along for this to be of any help,
but every now and then (as was the case in this puzzle) it can bring light.
Susan Webster
Canton, OH
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