Dissection Problems in PFCS/FCR

Much pioneering work on the subject of dissection problems using pieces formed of squares (now often called 'polyominoes') was done in the pages of The Problemist Fairy Chess Supplement (1930-6) and its continuation The Fairy Chess Review (1936-1958), during the years 1934-57. This work has not been fully appreciated because most of the results were published there in a coded form instead of by means of diagrams. This meant it was difficult for anyone who lacked the issue that contained the key (PFCS April 1937) to reconstruct the solutions.

Some time in the 1970s, after becoming a member of the British Chess Problem Society and seeing references to FCR in The Problemist I obtained a number of issues of the magazine from a London bookshop, and found them a mine of information, not only on variant chess but also on mathematical recreations such as knight's tours and dissection problems. However, it was some years later, thanks to the late Anthony Dickins, who provided a complete photocopied set of FCR to the BCPS library for use of its members, and later to John Beasley who allowed me to copy his own set of FCR, that I was able to supplement my own collection with photocopies of all the other issues.

By 1986 I had decoded most of the dissection results in FCR and in 1988 (as noted in issue 8+9 of my Games and Puzzles Journal page 124) I tidied up the notes of the work, drew out all the results by hand, and made photocopies available to a few interested correspondents. The results, titled Dissection Problems in PFCS/FCR occupied 63 A4 pages. This web-page is a summary of these notes including more detail, in particular the page numbers.

Diagrams of the solutions can be viewed by clicking on the problem numbers, or they can be seen on the separate themed pages in the Contents list for this site.

For an explanation of the Abbreviations and Notations used, for the Initials and Biographical Details of Contributors and for a Guide to Issue and Problem Numbers in PFCS/FCR see the Key to the Dissection Problems in PFCS/FCR.

#9/10 Dec/Feb 1934/5 p92/104-5 ¶1597 HDB introduces the 35 [6]s and asks if they can be arranged in 15x14 rectangle, TRD gives some notes on history of dissection problems, FK gives proofs of impossibility of the 15x14 rectangle.

#10/11 Feb/Apr 1935, p105/116 ¶1679 - ¶1680 - ¶1681 FK and WEL the [5]s forming rectangles 4x15, 5x12, 6x10, p108/117 ¶1704 HDB poses problem of dissecting 9x9 into [5]s + [4]s + [1], showing Roman Cross on Plinth.

#11/12 Apr/Jun 1935 p119/126 ¶1780 - 1781-2 WEL the [5]s forming 5x12, 6x10 with every piece abutting the edge, and 6x10 with 1x5 piece internal.

#12/13 Jun/Aug 1935 p128/135 ¶1844 FH the [5]s in 3x20 rectangle, ¶1845 WEL the 6x6 dissected into pieces of 8 different sizes each touching at least two edges.

#13/14 Aug/Oct 1935 p138/149 ¶1923 - also WEL and BZ (independently) the [5]s in 8x8 less corners, ¶1924 HDB the [5]s and 1x4 in 8x8.

#14 was a special issue on Swedish problemists: no new dissection problems.

#15 was on the work of C. M. Fox: no new dissection problems.

#16/17 Feb/Apr 1936, p172/182 ¶2171 - ¶2172 HDB [5]s + [4]s in 8x10, ¶2173 - ¶2176 DRD [4]s + [3]s + [2] in 2x14, 4x7 none/two internal, p173/183 ¶2199-2201 HDB [5]s + [4]s in 4x20 with all on edge, 1x5 internal, 1x5 and 1x4 internal.

#17/18 Apr/Jun 1936 p178/189 ¶2252 HDB [5]s + [4] in 8x8 with 7 not on edge.

#18/1 (Vol.3) Jun/Aug 1936 p188/p5, ¶2296 HDB [5]s + [4]s + [1] in 9x9 with one piece internal, ¶2297-8 WEL the 8x8 divided into 16 differing pieces with min/max cuts of edge.

#1/2 Aug/Oct 1936 p8/16, ¶2407 HDB 8x8 cut into all compact [6]s + [4]s, ¶2408 HDB 8x8 cut into all compact symmetric [6]s + [5]s, ¶2409 DRD 11 [5]s in triangle, ¶2410 GF [5]s + [4]s in 'diagonal square', diameter 7 with 5-square cross-shaped hole.

#2/3 Oct/Dec 1936 p19/26-7, ¶2483-5 HDB 5x16 in [5]s + [4]s all on edge with 1x5 internal or with 1x4 and 1x5 internal.

#3/4 Dec/Feb 1936/7 p29/38, ¶2554 HDB 8x8 board in all compact [6]s + [4]s, ¶2555 HDB 8x8 in all compact asymmetric [6]s + [5]s, ¶2556-7 HDB and WHRa (independently) [5]s + [4]s in Greek cross, ¶2558 DRD [5]s in 'castle'.

#4/5 Feb/Apr 1937 p41/51, ¶2620 HDB [5]s + [4]s making two shapes that will form 8 of the [5]s in quadrupled size, ¶2621 GF all compact [6]s + [4]s in 8x8 with four internal, ¶2622 HDB [6]s in triangle, ¶2623 BL enumeration of 4x4 in 4 pieces of 4 squares.

#5 Apr 1937, p46-7 'A Notation for Dissection problems' by TRD and WEL, p47 ¶2648-50 TRD 8x8 in [5]s and 2x2 proving 2x2 can occur in any position, F.Douglas and WEL report 108 pieces of 7 squares (number for 8 squares is incorrect).

#5/6 Apr/Jun 1937 p53/62-3, ¶2697 HDB 8x8 in all compact [6]s + [4]s with four [6]s internal, ¶2698 - also FH 12x17 in 34 [6]s omitting one 2:4 chequered piece (solutions to all 11 cases by GF were given).

#6/7 Jun/Aug 1937 p65/74 ¶2777-8 HDB 8x8 + 5x5 joined h2-6 in all pieces [1] to [5].

#7/8 Aug/Oct 1937 p76/84, ¶2854-6 HDB 8x8 + 5x5 joined h1-5 in all pieces [1] to [5], ¶2857 HF 8x8 + 5x5 joined at corner in all pieces [1] to [5].

#8/9 Oct/Dec 1937 p86/96, ¶2924 - also HDB [5]s + [4]s in 4x8 and 4x12 simultaneously, ¶2925-6 WHRe and GF 8x8 + 5x5 joined h1-4 in all pieces [1] to [5].

#9/10 Dec/Feb 1937/8 p99/107, ¶3026-30 HDB [4]s on 5x5, ¶3031 DHH [5]s on 8x8 with 4 holes on diagonal.

#10/11 Feb/Apr 1938 p109/117 ¶3089 HDB long [6]s in 9x18.

#11/12 Apr/Jun 1938 p119/127, ¶3162 HDB all compact [6]s + [5]s in 8x11, ¶3163 DHH [5]s in 8x8 with four holes in square, ¶3164 WHRe the [1] to [5] pieces in letters GF.

#12/13 Jun/Aug 1938 p129/138, ¶3228 HDB [4]s + [5] on 5x5, ¶3229 HDB [5]s + 1x4 on 8x8 all on edge, ¶3230-1 TRD [5]s + [4] on 8x8 with one internal.

#13 Aug 1938 p142 JN total of 369 pieces of 8 squares is confirmed (previous discussion appeared in #5 Apr 1937 p47; #6 Jun 1937 p67; #12 Jun 1938 p131).

#13/14 Aug/Oct 1938 p140/147, ¶3305 HDB [5]s in L width 4, ¶3306 HDB [5]s + [4]s in L width 4, ¶3307 WJ arithmetical problem.

#14 Oct 1938 p152 JN total of 1285 pieces of 9 squares is confirmed.

#14/15 Oct/Dec 1938 p151/156-7, ¶3399-400 WEL asymmetric [6]s in 5x24 and 10x12, ¶3401 TRD asymmetric [6]s in two 5x12.

#15/16 Dec/Feb 1938/9 p160/171, ¶3478-9 WEL asymmetric [6]s in 6x20 and 8x15, ¶3480 TRD asymmetric [6]s in two 6x10, ¶3481-3 HDB [5]s + [4] in 8x8 with one internal.

#16/17 Feb/Apr 1939 p174/186, ¶3569 HDB [5]s in 'rook' shape.

#17 April 1939 was a special Dutch issue and had no dissections.

#18/1 (Vol.4) Jun/Aug 1939 p198/p.9, ¶3742 HDB [5]s + [4]s in 4x9 and 4x11 simultaneously, ¶3743 FH and DHH (independently) [5]s in 8x8 with four holes in square.

#1 Aug 1939 special issue on Hungary, no new dissection problems.

#2 Oct 1939. No dissection problems in this issue at the outbreak of the war.

#3 Dec 1939 (dated 28 November) a special TRD 50th birthday celebration with 68 pages plus cover. Due to the large number of problems the solutions of the dissection problems were delayed to #6 Jun 1940, and no further new problems appeared until #7 Aug 1940.

#3/4 Dec/Feb 1939/40 p28/75 ¶3930 WHRa asked how many fundamentally different forms can be made from 5 equal cubes fitted face to face? No conclusive answer was given. The question was revisited in Vol.6 #18 June 1948 p141-2 where the total was given as 23 or 29 depending on the criteria used.

#3/6 Dec/Jun 1939/1940, p43/93 ¶4142 HDB H for Happy Birthday, ¶4143 HDB 27x6 from non-compact [6]s, ¶4144-8 RJF 64-square 'pyramids' from [5]s + [4], ¶4149 RJF [5]s enclose maximum area, p44/93 ¶4150 FH Frame 18x18 width 3 from the 36 chequered [5]s, ¶4151 OW [5]s form a monument of specified castle-like design, p44/93-4 ¶4152-3 FH article on 'Sam Loyd's 18-Piece Dissection' with detailed analysis and two problems, p44 ¶4154 JN article 'The Colossal Count' an attempt to count the 10-square pieces, total reported 4654 is one short.

#7/8 Aug/Oct 1940 p100/114 ¶4567 HDB 5x6 in [4]s + [5] duplicated.

#8/9 Oct/Dec 1940 p110/121 ¶4615-8 TRD [5]s + [4] in 8x8 with maximum not on edge, one case has an improved solution by SHH.

#10/11 Feb/Apr 1941 p128/138, ¶4711 HDB 8x10 with [5]s and [4]s one not on edge, ¶4712 RJF [5]s plus double-size piece form same shape quadrupled.

#11/12 Apr/Jun 1941 p136/146, ¶4774 HDB, ¶4775 RJF,.continuations.

#12/13 Jun/Aug 1941 p144/154, ¶4843 HDB, ¶4844 RJF, continuations.

#13/14 Aug/Oct 1941 p152/161, ¶4893 HDB, ¶4894 RJF, continuations.

#14/15 Oct/Dec 1941 p160/171, ¶4957-8 HDB, ¶4959 RJF, continuations.

#15/16/17 Dec/Feb/Apr 1941/2 p166-7/178/187, ¶4985 - ¶4986 - ¶4987 - ¶4988 - ¶4989 HDB [6]s in serrated squares with diagonal symmetry, ¶4990 - ¶4991 - ¶4992 - ¶4993 HDB [6]s in 'castles' with lateral symmetry, ¶4994 - ¶4995 HDB [6]s in 'mines' with lateral symmetry, ¶4996 - ¶4997 HDB [6]s in serrated squares with lateral symmetry, all to show different colour differences. The solutions were spread over two issues.

#16/17 Feb/Apr 1942 p176/187, ¶5050 HDB [5]s in 'V for Victory', ¶5052 TRD [5]s in reversed-out 'V for Victory'.

#17/18 Apr/Jun 1942 p187/196, ¶5139-40 HDB, ¶5141 RJF, continuations.

#18/1 (Vol.5) Jun/Aug 1942 p195/p.6, ¶5210-11 HDB, ¶5212 SHH, continuations.

#1/2 Aug/Oct 1942 p5/14, ¶5270-1 HDB, ¶5272 SHH, continuations.

#2/3 Oct/Dec 1942 p12/22, ¶5338-9 HDB,¶5340 SHH, continuations.

#3/4 Dec/Feb 1942/3 p21/29, ¶5397-8 HDB end of series, ¶5399 TRD smallest area from which any [5]-piece can be cut.

#4/5 Feb/Apr 1943, p26/37 ¶5418 HDB [5]s + [4]s in quartered 8x10 with 2x2 central, p28/37-8 ¶5448 TRD the [5]s and T-shaped 4-piece in 8x8 with inset 3x3, plus other solutions showing all possible positions of the T-piece.

#5/6 Apr/Jun 1943 p36/46, ¶5498 HDB [5]s + 4[4]s in quartered 8x10 with central 2x2 hole, ¶5499 TRD the [5]s and L-shaped 4-piece in 8x8 with inset 3x3, plus other solutions showing all possible positions of the L-piece.

#6/7 Jun/Aug 1943 p45/55, ¶5590 TRD [5]s + [4] in 8x8 showing inset 5x5.

#7/8 Aug/Oct 1943 p53/62-3, ¶5656 HDB [5]s + [4]s in 8x10 with minimum on edge, ¶5657 TRD [5]s + [4] in 8x8 with inset 2x7, ¶5658 RJF [5]s + [4] in 8x8 anchor ring with no 8-unit cut.

#8/9 Oct/Dec 1943, p58/69 ¶5668 HDB [6]s in V-shape, p61/70 ¶5727-31 TRD [5]s + [4] in 8x8 with inset 3x8.

#9/10 Dec/Feb 1943/4 p69/78 ¶5800-4 TRD [5]s + [4] in 8x8 with inset 5-piece '11' (a1234b1) doubled.

#10/11 Feb/Apr 1944, p74/86 ¶5819 - ¶5820 HDB all but one [6] can be made from three pieces, with the 35 [6]s plus one duplicate form these pieces magnified 6 times, p76/87 ¶5860-4 TRD [5]s + [4] in 8x8 with inset 5-piece '12' (a1234b2) doubled.

#11/12 Apr/Jun 1944 p85/94, ¶5927-8 HDB [5]s + [4]s in 8x10 with minimum on edge, ¶5929-33 TRD [5]s + [4] in 8x8 with inset 5-piece '13' (a123b12) doubled in corner, ¶5934 RJF cut fewest [5]s out of 8x8 until no more can be cut.

#12/13 Jun/Aug 1944 p92/102, ¶6010 HDB use two sets of [5]s and two [2] to form reversed out cross of Lorraine, ¶6011-5 - also TRD [5]s + [4] in 8x8 with inset triangle in corner, ¶6016 RJF, WEL, HP, WJT (solvers of 4142) [5]s forming another H.

#13/14 Aug/Oct 1944, p100/111 ¶6087 HDB another reversed out cross of Lorraine, p101/111 ¶6088 - ¶6089 TRD [5]s + [4] in 8x8 with inset triangle and rectangle or square.

#14/15 Oct/Dec 1944 p109/119, ¶6167 HDB [6]s + [5]s in a cross of Lorraine, ¶6168 TRD [5]s + [4] in 8x8 with inset 5-piece '13' (a123b12) doubled, not in corner.

#15/16 Dec/Feb 1944/5 p117/126, ¶6227 HDB [6]s + [5]s in ornate cross of Lorraine, ¶6228 TRD [5]s + [4] in 8x8 with inset triangle not in corner.

#16/17 Feb/Apr 1945 p124/133-4, ¶6296 WHRe more cases of 6168, ¶6297 TRD [5]s + [4] in 8x8 with inset 9-square triangle, ¶6298 RJF transforming [5]s into each other in sequence, ¶6299 HDB [5]s + [4] in 8x8 anchor ring, no cut longer than 5 units.

#17/18 Apr/Jun 1945 p132/142, ¶6375-6 HDB [6]s forming reversed out cross of Lorraine two types, ¶6377 K.Benjamin further case of ¶6228, ¶6378 - also TRD [5]s + [4] in 8x8 with two inset 10-square triangles, ¶6379 FH [5]s + [4] in 8x8 with inset 4x6.

#18/2 (Vol.6) Jun/Oct 1945/6 p140/p9 (misnumbered 149), ¶6456 HDB 9 [5]s to form all the [5]-shapes magnified three-fold, ¶6457 TRD 4 [5]s to form [5]-shapes magnified two-fold.

#1/3 Aug/Dec 1945 p3/17 ¶6518 HDB [5]s + [4]s + [1] in 9x9 with one piece internal and [1] in corner. [In the solution to ¶2296 these results were attributed to GF, but perhaps HDB made a complete set of solutions as well.]

#2/3 Oct/Dec 1945 p8 (misnumbered 148)/p18, ¶6573-4 HDB and LRC further cases of 6379, ¶6575 RJF box to pack in the [5]s in three layers fitting exactly.

#3/4 Dec/Feb 1945/6 p16/26, ¶6628 HDB [5]s in 9x9 minus 21-square triangular corner, ¶6629 RJF all pieces [1] to [5] spell HELPMATES, ¶6630 FH all narrow [6]s + [5]s in 9x12.

#4/5 Feb/Apr 1946, p24/34 ¶6693 HDB [5]s + [4]s in 10x10 with holes, ¶6694 FH oddly chequered [6]s plus one duplicate in 6x12, p24-5/34 ¶6695 - ¶6696-8TRD a study in 'transfers' [5]s + [4] in 8x8 with inset 14-square areas in which two [5]s can be moved around, so the remaining 4 squares form different [4]s, ¶6699 TRD five consecutive transfers, ¶6700 TRD formation with L-tetromino and 8 [5]s showing transfers

#5/6 Apr/Jun 1946, p32/41-2 ¶6759-61 RJF [5]s used to cover 1x1x1, 2x2x2 and 3x3x3 boxes, p32/42 ¶6762 - ¶6763 - ¶6764 - ¶6765 - ¶6766 FH the 24 evenly chequered [6]s in 6-fold magnifications of each of the [4]-shapes.

#6/7 Jun/Aug 1946, p40/49 ¶6841-3 RJF [5]s used to cover 2x2x7, 10[5]s + [4] on 3x3x3 lapping or abutting edges, p40/49-50 ¶6844 ¶6845 - ¶6846 FH [6]s plus duplicate forming 6-fold magnification of the added piece.

#7/8 Aug/Oct 1946, p46/57 article with account of HDB's idea of 'hollow rectangles' (HRs) ¶6883 TRD [4]s + [3]s + [2] in HRs, ¶6884 - also TRD [5]s in HRs, ¶6885 HDB [6]s + [5]s cut from 3x3 in HRs, ¶6886 HBD [6]s + [5]s + [4]s cut from 3x3 in HRs, p48/58 ¶6925 RJF all pieces [1] to [5]s covering surface of column 13x1x1 plus plinth, ¶6926 - ¶6927 - ¶6928 FH continuation of 6844.

#8/9 Oct/Dec 1946 p56/66, ¶6999 TRD two sets of narrow [5]s in HRs, ¶7000 HDB evenly chequered [6]s in HRs, also by FH, ¶7001 - also - also FH continuation of ¶6844, ¶7002 RJF 4[5]s + 1[4] covering a root-5 edge cube, except at corners.

#9/10 Dec/Feb 1946/7 p65/74, ¶7090 TRD [5]s + [3]s in HRs, ¶7091 HDB compact [6]s + compact [5]s + [4]s in HRs, ¶7092 - also FH conclusion of ¶ 6844.

#10/11 Feb/Apr 1947, p71/81 ¶7124 FH [5]s cover two root-5 cubes simultaneously, pp.72/82 ¶7158 HDB [5]s + [4]s form christmas tree.

#11/12 Apr/Jun 1947 p80/90 ¶7250 - also TRD [5]s + 4[4]s in 9x9 hollow square, ¶7251 HDB and TRD [5]s + [4]s in HRs, ¶7252 FH [6]s in three different sized figures of same 6-square shape simultaneously, using shape '24' (a12345,b2).

#12/13 Jun/Aug 1947 p89/99, ¶7324 TRD [5]s + 3[4]s in 8x10 HRs, ¶7325 HDB [6]s + [3]s in HRs width 4, ¶7326 FH continuation, [6]s in triple shape '27' (a1234,b13).

#13/14 Aug/Oct 1947 p97/108 ¶7386 TRD [5]s + 3[4]s in 7x11 HRs, ¶7387 HDB [6]s + [3]s in HRs width 6, ¶7388 FH continuation, [6]s in triple shape '33' (a123,b234), ¶7389 EL arithmetical broken boards puzzle.

#14/15 Oct/Dec 1947 p106/116, ¶7459 TRD [5]s + 3[4]s in HRs 6x12, ¶7460 FH continuation, [6]s in triple shape '37' (a123,b12,c1), ¶7464 EL arithmetical broken boards puzzle.

#15/16 Dec/Feb 1947/8 p114/123, ¶7521 FH and ¶ 7522 TRD narrow [6]s + narrow [5]s in HRs width 3, ¶7523 THWillcocks: squaring the square problem.

#16/17 Feb/Apr 1948, p121/131 ¶7560 D.Nixon [5]s one unit thick in 3x4x5 solid, p122/131 ¶7590 HDB cover root-5 cube, except corners, with 4[5]s and 1[4], another case of 7002, ¶7591 HDB cover root-10 cube with all the [5]s, ¶7592 FH continuation, [6]s in triple shape '39' (a123,b2,c23), ¶7593 - also TRD unsymmetrical [6]s in HRs width 4.

#17/18 Apr/Jun 1948 p130/140 ¶7652 WEL 36-square triangle in two sets of [4]s less one piece. (This is an issue devoted to unpublished problems by dead composers)

#18 Jun 1948 p141-2 'Space Dissection' article, revisiting ¶3930 and counting the 23 fundamentally different 5-cube pieces, or 29 counting 6 enantiomorphous pieces. FH counted 77 pieces of 6 cubes. Various dissection results mentioned but not given in detail.

#18/1 (Vol.7) Jun/Aug 1948 p138/6 (misnumbered 98) ¶7726 - also TRD unsymmetrical [6]s in HRs width 5, ¶7727 - also HDB [6]s + [5]s in HRs width 5, ¶7728 FH continuation, [6]s in triple shape '40' (a234,b12,c2).

#1/2 Aug/Oct 1948 p4/14 (misnumbered 96/106) ¶7792 - also TRD [5]s in 'Half-Hollow Rectangles' (HHRs), ¶7793 HDB [[5]s + [3]s in HHRs, ¶7794 FH continuation, [6]s in triple shape '44' (a12b123c2), p5/14 (97/106) ¶7795 THW squaring the square problems, p.8/16 (100/108) JN on counting solid pieces formed of cubes, sizes up to 7, but further disputation of the results on solutions page.

#2/3 Oct/Dec 1948 p14 (misnumbered 104)/p22 ¶7864 HDB [5]s + [4]s in bisected HHRs, ¶7865 FH continuation, [6]s in triple shape '47' (a34b123c2), p15 (misnumbered 105)/p22 7866 RJF dissection of 8x8 into 2x2 and 12[5]s, not necessarily different, with minimum length cuts, p16(108)/22 ¶7879 A.W.Baillie on minimum number of layers for solid n-cubes (further there is a correction in #4 Feb 1949 p31).

#3/4 Dec/Feb 1948/9 p20/29, ¶7939 HDB evenly chequered [6]s in bisected HHRs, ¶7940 FH continuation, [6]s in triple shape '51' (T: a123b2c2d2).

#4/5 Feb/Apr 1949, p27/37 ¶7976-7 HDB [6]s in one shape + [5]s in another that will combine to make a 15x18 rectangle or a stepped parallelogram, p.28/38 ¶7995FH continuation, [6]s in triple shape '53' (a4b1234c2), ¶7996 RJF dissection of 8x8 into 2x2 and 12[5]s, not necessarily different, showing 90 degree rotary symmetry, p31 Note by 'Miss E. Meredith' (TRD) citing article in Mathematical Gazette about pieces '37' (a123b23c3) and '38' (a123b13c3) divided into parts similar to the whole. (Solution not given.).

#5/6 Apr/Jun 1949 p36/46 ¶8079 HDB [6]s + [5]s + [4]s, all cut from 3x3, in bisected HHRs, ¶8080 FH conclusion, [6]s in triple shape '55' (cross a3b1234c3).

#6/7 Jun/Aug 1949 p44/53 ¶8144 HDB evenly chequered [6]s in HHRs, ¶8145 FH [6]-pieces doubled using a component of the same shape as the whole.

#7/8 Aug/Oct 1949 p52/62 ¶8223 HDB [5]s in HHRs, ¶8224 FH [5]s + [4] in 4-fold magnification of the [4]-piece.

#8/9 Oct/Dec 1949 p60/87 ¶8297 HDB narrow [6]s and narrow [5]s in HHRs, ¶8298 WHRe [6]s + [5]s in triple shape '38' (a123b1c12).

#9/14 Dec/Oct 1949/50 p86/122. The December issue (actually dated 28 November) was a 'diamond jubilee' special for TRD's 60th birthday. The solutions were delayed due to the death of HDB. ¶8551 WHRe [6]s + [5]s in shape of 6 and 0 simultaneously, ¶8552 Mrs HDB [6]s in shape of L and X simultaneously.

#10/14 Feb/Oct 1950 p90/122 ¶8555 FH which shapes formed of two rectangles can be made with the [6]s, ¶8556 FH longest such double rectangle, ¶8557 FH which shapes formed of one rectangle cut from another can be made with the [6]s, ¶8558 FH [6]s in square with central rectangular hole, ¶8559 HDB [6]s in three joined squares,¶8560 HDB "6 of the 5-pieces are taken at random, and all the 6-pieces. What chance is there of forming a stepped square (diagonal 23) with a stepped square (diagonal 7) cut out at 1-unit distance from centrally?".

#12/15 Jun/Dec 1950 p108/131 ¶8725 EL arithmetical broken boards puzzle, ¶8728 HDB [6]s in two equal joined triangles, ¶8729 FH [6]s + duplicate piece '55' forming sixfold magnified shape '56'.

#13/16 Aug/Feb 1950/51 p117/139 ¶8793 - 8794 HDB [5]s in HHRs widths 4 and 5, ¶8795-6 HDB even-chequered [6]s in HHRs widths 4 and 6.

#14/16 Oct/Feb 1950/51 p128/140 ¶8848 HDB [5]s + [4]s cover exterior of double cube (side 2root2)

#15/17 Dec/Apr 1950/51 p134/150 ¶8912 HDB [6]s in symmetrical figure formed of rectangle + square.

#16/18 Feb/Jun 1951, p142/158 ¶8940 FH [6]s + [5]s in triple shape '49' with [5]s in middle shape largest shape or both equally, p144/158 ¶8971 TRD [1] to [4] pieces enclosing maximum area, ¶8972 THW squaring the rectangle, ¶8977 FH a monument made with the solid [5]s, in memory of HDB.

#17 Apr 1951 no dissections.

#18/2 (Vol.8) Jun/Feb 1951/2 p157/16 ¶9104 J.Sunyer, arithmetical question, ¶9105 THW squaring the rectangle.

#18/3 (Vol.8) Jun/Apr 1951/2 p157/26 ¶9106 FH [6]s + [5]s showing shape '14' (C: a123b13) in four different sizes simultaneously.

#1/2 Aug/Feb 1951/2 p4/17 ¶9170 THW squaring the rectangle.

T. R. Dawson died 16 December 1951. The February 1952 issue was edited by C. E. Kemp. Then Dennison Nixon became the editor until 1956.

#3/5 Apr/Aug 1952 p25/37 ¶9235 HDB [6]s illustrate a 'spreading chestnut tree'.

#4/6 Jun/Oct 1952 p31/45 ¶9287 HDB [5]s + [4]s + [1] with one piece internal, unit square at b1.

#5/7 Aug/Dec 1952 p36/52 ¶9331 WS [6s]s in 15x15 with three holes in shape of 5-square Greek crosses.

#6/8 Oct/Feb 1952/3 p43/60 ¶9389 WHRe [6]s + [5]s showing shape '17' (W: a23b12c1) in four different sizes simultaneously.

#7/9 Dec/Apr 1952/3 p50/68 ¶9442 FH [6]s in 5 congruent shapes (5x9 rectangles less 3 cells) simultaneously. ¶9443 FH [6]s + [5]s in 5 congruent shapes (6x9 rectangles) simultaneously.

#8/10 Feb/Jun 1953 p56/75 ¶9455 WS [6]s in New York or Churchillian profile.

#9/11 Apr/Aug 1953 p66/85 ¶9543 WS [5]s forming 'teapot', ¶9544 WHRe [6]s + [5]s showing shape '11' (a1234b1) in four different sizes simultaneously.

#10/12 Jun/Oct 1953 p74/93 ¶9602 - ¶9602-3 PBVD and WS [5]s in 8x8 with 4 missing squares in square.

#13/15 Dec/Apr 1953/4 p99/118 ¶9783 WS [6]s in 'christmas tree'.

#15/17 Apr/Aug 1954 p116/136 ¶9884 FH [5]s in 5x11 omitting one.

#17/1 (Vol.9) Aug/Dec 1954 p134/p.9 ¶10003 WS [5]s in form of a 'key', ¶10004 WHRe [6]s + [5]s showing shape '13' (a123b12) in four different sizes simultaneously.

#18/2 (Vol.9) Oct/Feb 1954/5 p143/p19 ¶10057 FH [5]s in 6x10 with symmetric crossroads.

#1 Dec 1954 p2-4. Article on 'Dissection' by W. Stead, including a full page of drawings of 38 outstanding results achieved to that date. See: ¶2 + 8, ¶6, ¶7, ¶13 + 14, ¶15 + 16, ¶18 + 24, ¶20, ¶21, ¶26, ¶27, ¶28, ¶29, ¶30, ¶32, ¶33, ¶34 (by FH), ¶35, ¶36, ¶37, ¶38 (by FH).

#1/3 Dec/Apr 1954/5 p4/25 ¶10067 WS [5]s in three congruent shapes simultaneously, ¶10068 FH [5]s + [4]s in 8x10 with symmetric crossroads.

#2/4 Feb/Jun 1955 p17/34 ¶10152 FH [5]s + [4]s + [1] in 9x9 with symmetric crossroads.

#3/5 Apr/Aug 1955, p24/43 ¶10200 WS 5x5 less centre cell covered by 4 [6]-pieces of one or two kinds, p.25/43 ¶10201 FH evenly chequered [6]s in shape of 6-square cross (shape '55') with cross-shaped hole.

#4/6 Jun/Oct 1955 p32/50 ¶10254 GJB [5]s + [4]s + [1] in 81-square triangle, ¶10255 WS 8x8 less corners covered with 12 [5]s or 10 [6]s of one or two kinds.

#5/7 Aug/Dec 1955 p40/59 ¶10302 WS 8x8 minus centre 4 covered with 10 [6]s all alike, 10x10 minus 4 corner or centre cells covered with 16 [6]s all alike, ¶10303 FH evenly chequered [6]s in shape '56' (a3b1234c2) with central hole of same shape.

#6/8 Oct/Feb 1955/6 p48/66 ¶10347 GJB even [6]s + piece '51' (T: a1b1234c1) in shape of '51' with added piece symmetrically placed, ¶10348 WS continuation of 10255, 10302.

#7/9 Dec/Apr 1955/6 p56/75 ¶10396 GJB 25 [6]s in 'christmas cracker', ¶10397 WS 8x8 less 4 cells like b2 covered with 12[5]s or 10[6]s of two kinds.

#8/10 Feb/Jun 1956, p64/83 ¶10439 GJB even [6]s + piece '27' (a1234b13) in shape of '27' with added piece in corner, p65/83 ¶10450 WS shortest closed loop from which any of the linear [6]-pieces can be cut, ¶10451-2 WS linear [6]-pieces in 6x13, branching [6]-pieces in 6x14, ¶10453 WS linear and branching [6]-pieces in 9x18, ¶10454 WS [5]s + clumped [6]s in two 6x9, ¶10455 WS [5]s + clumped [6]s in square 12x12 with 6x6 hole.

#9/11 Apr/Aug 1956 p73/92 ¶10498 FH [6]s + one duplicate in three 6x12 rectangles.

#10/12 Jun/Oct 1956 p81/102 ¶10544-6 WS [5]s in 8x8 omitting squares where 4 rook + nightriders will guard all 64 squares.

#12 Oct 1956 p100 ¶10637-9 WS [5]s in 8x8 omitting four squares in various positions (no solutions published).

#13/15 Dec/Apr 1956/7 p109/126 ¶10689-91 WS2 and GJB clumped [6]s + [5]s in 'christmas goose' and 'christmas pudding' and 'christmas candle'.

#14 Feb 1957 p115 reports the decision of the editor C. E. Kemp to discontinue the dissections. FCR ran for a further 7 issues, ending with #21 (misnumbered 20) April 1958.