ç Index to Chessboard Dissection Problems

# The 6-Square Pieces: with Additions

Here we gather constructions with 6-pieces that use more than the full set of 35.

## 36: The [6]s Plus One

F. Hansson. The 35 [6]s plus an extra oddly-chequered piece, form a sixfold magnification of the added piece, without crossroads or cuts at reentrant angles. There are 11 cases:

F. Hansson (FCR Jun/Aug 1946 ¶6844). Piece 24 (6,3).

F. Hansson (FCR Jun/Aug 1946 ¶6845). Piece 27 (6,7).

F. Hansson (FCR Jun/Aug 1946 ¶6846). Piece 33 (6,11).

F. Hansson (FCR Aug/Oct 1946 ¶6926). Piece 37 (6,15).

F. Hansson (FCR Aug/Oct 1946 ¶6927). Piece 39 (6,19).

F. Hansson (FCR Aug/Oct 1946 ¶6928). Piece 40 (6,27).

F. Hansson (FCR Oct/Dec 1946 ¶7001). Piece 44 (6,28).

F. Hansson (FCR Oct/Dec 1946 ¶7001). Piece 47 (6,30).

F. Hansson (FCR Oct/Dec 1946 ¶7001). Piece 51 (6,22).

F. Hansson (FCR Dec/Feb 1946/7 ¶7092). Piece 53 (6,23).

F. Hansson (FCR Dec/Feb 1946/7 ¶7092). Piece 55 (6,32).

The next example is not part of the above series, since the piece used is not the same shape as the whole dissection.

F. Hansson (FCR Jun/Dec 1950 ¶8729). Shape 56 (6,33) using two pieces 55 (6,32).

F. Hansson (FCR Dec 1954 ¶38 in article by W. Stead). Using one duplicated [6] - one of the oddly chequered pieces - construct a 15×15 showing a 9×9 square enclosing a 3×3 hole.

Multiple Shapes

H. D. Benjamin (FCR Feb/Apr 1944 ¶5820) using all the [6]s and one duplicate fit the pieces together in three parts that will join together to form all the 6-square shapes, magnified 6 times, except the 1×6. All pieces, except the cross-shaped piece 55 (6,32) can be made without crossroads. In particular the pieces can make the shape of the duplicated piece 39 (6,19) with the duplicated piece (or a hole of the same shape) in the same orientation as the whole.

F. Hansson (FCR Feb/Apr 1946 ¶6694} forms a 6×12 (domino shape) rectangle using the 11 oddly-chequered [6]s plus one duplicate. Later (FCR Apr/Aug 1956 ¶10,498) he extended this result to show all the [6]s plus one piece 39 (6,19) forming three simultaneous rectangles 6×12. The first 6×12 can be combined with the sextuplicated copies of the [4]s formed from the 24 evenly chequered pieces to form sextuplicated copies of all the 35 [6]s.

## 70: The Double [6] Set

F. Hansson (FCR Dec 1954 ¶34 in article by W. Stead). Sent as a christmas card for 1953. A hollow square 26×26 with 16×16 hole. Using two complete sets of [6] pieces, one for each half.

W. Stead (FCR Dec 1954 ¶36). 5×84 rectangle from two complete sets. Left half only shown.

W. Stead (FCR Dec 1954 ¶37). 15×28 rectangle from two complete sets.