Catalogue of Asymmetric Closed Knight's Tours of the 6 by 6 Board

This page shows those with 6 and 10 slants.

Asymmetric with 6 Slants (total 304)

(None of the symmetric tours have 6 slants.)

Two nets are toured in an unbroken eight-move path, while the other two nets are toured in two parts. Since there is one even slant and five odd slants a pair of slants must meet on one of the centre cells (forming an angle of type a, c, f or m). This means that one of the broken nets must be toured as a seven-move path of straights and an isolated cell. The numbers of these four types are: a-type 80, c-type 32, f-type 136, m-type 56. The tours in this class can be further subclassified according to whether the two unbroken nets are toured successively (total 96) or are separated (total 208).

The tours are shown here in small format (as originally drawn in Lotus AmiPro a few years ago. I hope eventually to convert them all to larger format as in the previous parts, but this may take some time). They are grouped into windows of 50 or fewer tours, except for the last group of 56.

(a type) total 80: first 50.

(a-type): remaining 30:

(c type) total 32.

(f type) total 136, first 50:

(f type) second 50:

(f type) remaining 36:

(m type) total 56:

Asymmetric with 10 Slants (total 288)

(None of the symmetric tours have 10 slants.)

aaa type 9.

aac type 52.

aaf type 33.

aam type 8.

acc type 11.

acf type total 69, first 40.

acf type — remaining 29.

acm type 13.

aff type 35.

afm type 11.

ccf type 9.

ccm type 1.

cff type 19.

cfm type 6.

cmm type 1.

fff type 8.

ffm type 3.

Impossible are: amm, ccc, fmm, mmm types.

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