The 10th Pentacube Contest 1999 and CFF Contest 37. Build the figure "Pentacube Frame on a Board" with all 29 pentacubes. Each number says, how many cubes are stacked. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Send your solution to: Rik van Grol = mailto:rvgrol@hotmail.com Hilvoordestraat 14, 2284 BK Rijswijk, NL, +31-70-3937264 The pentacube contest has been founded by Ekkehard Kuenzell, Schoenrathstr. 79, D-52066 Aachen, Germany, +49-241-58881 He selected this jubilee problem year ago. Deadline: >>>>> 1999-04-25 <<<<< Prizes: Three prices will be made available from the CFF prize list. Notation for the Pentacubes: The notation follows a mnemonic system and is easily recognized by the solution of the following pentacube problem. The system is explaned in [K"unzell]. 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 a pentacube problem 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 11 12 22 22 22 72 72 72 90 51 51 51 71 71 71 one solution 10 12 42 42 22 34 34 72 20 20 51 82 82 71 70 (bottom layer) 10 12 12 33 41 41 34 34 90 20 35 35 70 70 70 10 12 60 33 33 36 36 30 30 20 20 35 50 70 40 10 37 60 81 33 36 32 32 30 30 31 50 50 50 40 10 37 60 81 81 81 21 32 32 30 31 31 50 61 61 11 22 41 72 90 51 82 71 (top layer) 11 42 41 34 90 35 82 40 11 42 41 36 90 35 82 40 11 42 33 36 80 31 13 40 37 60 21 32 80 31 13 61 37 37 60 81 21 21 21 80 80 80 13 13 13 61 61 The list of figures of the last contests: (number of participants) The 1st Pentacube Contest 89/90 (10) 2 2 2 2 2 2 2 4 4 4:4 4 2 n:= the two bottom cubes are missing of 2 4 6 6:6 4 2 the pile of height n. 4:6:b:6:4: 2 4 6 6:6 4 2 b = 11 2 4 4 4:4 4 2 2 2 2 2 2 2 Figure: "Monument" The 2nd Pentacube Contest 90/91 and CFF Contest 6 (5) 2 Figure: "Jagged Square Ring" 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 1 1 1 2 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 2 1 1 1 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 The 3rd Pentacube Contest 91/92 and CFF Contest 14 (6) 5 5 5 5 5 5 5 Figure: "Open Box" 5 1 1 1 1 1 5 5 1 1 1 1 1 5 5 1 1 1 1 1 5 5 1 1 1 1 1 5 5 1 1 1 1 1 5 5 5 5 5 5 5 5 The 4th Pentacube Contest 92/93 (special CFF problem see below) (12) 1 1 1 1 1 1 1 1 1 Figure: "Mound" 1 2 2 2 2 2 2 2 1 1 2 3 3 3 3 3 2 1 1 2 3 2 2 2 3 2 1 1 2 3 2 1 2 3 2 1 1 2 3 2 2 2 3 2 1 1 2 3 3 3 3 3 2 1 1 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 see [Farhi, figure 127] and CFF Contest 18 1 2 3 4 5 6 5 4 3 2 1 Figure: "Cloven Mountain" 1 2 3.4.5.5.5.4.3.2 1 1 2 3.4 4 4 4 4 3.2 1 n.= the bottom cube is missing of 1 2 3.3.3.3.3.3.3.2 1 the pile of height n. 1 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 The figure must be stable. The 5th Pentacube Contest 93/94 and CFF Contest 25 (16 + 2 incorrect) 1 1 1 1 1 1 1 1 1 1 1 Figure: "Hip Roof" 1 2 2 2 2 2 2 2 2 2 1 1 2 3 3 3 3 3 3 3 2 1 1 2 3 4 4.4.4.4 3 2 1 n.= the bottom cube is missing of 1 2 3 3 3 3 3 3 3 2 1 the pile of height n. 1 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 The figure must be stable. The 6th Pentacube Contest 94/95 and CFF Contest 26 (16) 5 Figure: "Nine Slices" 4 5 4 3 4 5 4 3 2 3 4 5 4 3 2 1 2 3 4 5 4 3 2 1 2 3 4 5 4 3 2 3 4 5 4 3 4 5 4 5 see [Farhi, figure 105 "stadium"] The 7th Pentacube Contest 95/96 and CFF Contest 29 (20) 3 3 3 Figure: "Hollow Cube Pyramid" 3 3.3 3 3.3 3 3 3 6 6.6 3 3 3 n.= the bottom cube is missing of 3 3.3.6.6^6.3.3.3 the pile of height n. 3 3 3 6 6.6 3 3 3 3 3.3 n^= only one cube is in this pile. 3 3.3 It is at height n. 3 3 3 The figure must be stable. The 8th Pentacube Contest 96/97 and CFF Contest 31 (8) Figure: "pentacube plattform" 1 2 3 4 3 2 1 2 3 4 4 4 3 2 3 4 4 4:4 4 3 n:= the two bottom cubes are missing of 4 4 4:4^4:4 4 the pile of height n. 3 4 4 4:4 4 3 2 3 4 4 4 3 2 n^= only one cube is in this pile. 1 2 3 4 3 2 1 It is at height n. The figure must be stable. The 9th Pentacube Contest 97/98 and CFF Contest 33 (8). Figure: "top of tower" Each number says, how 1 2 3 4 3 2 1 many cubes are stacked. 2 3 4 5 4 3 2 3 4 5 6 5 4 3 This top of a tower consits of 175 cubes. 4 5 6 7 6 5 4 To build it up with the 145 cubes of the 29 3 4 5 6 5 4 3 pentacubes leaves you a space of 30 cubes 2 3 4 5 4 3 2 to be placed in the interior of the structure. 1 2 3 4 3 2 1 You may locate these empty cubes at any place you want. But there is one condition: The structure must be selfsupporting and resist even a strong pressure on the top of it. Some References: [CFF] Cubism For Fun CFF is a newsletter published by the Nederlandse Kubus Club NKC (Dutch Cubists Club). It appears three times a year (Feb., July, Oct.). Yearly membership fee is now NLG 30.- (Dutch Guilders) which amounts to approximately $ 20.-. Institutional membership is also possible. Information is available from the editor: Rik van Grol = mailto:rvgrol@hotmail.com Hilvoordestraat 14, 2284 BK Rijswijk, NL, +31-70-3937264 http://www.crosswinds.net/~cubismff/ [Farhi] Sivy Farhi, Pentacubes, 1981, 5th Edition, 70 pages, Pentacube Puzzles Ltd, 1220 Deer Trace Court Madisonville, KY 42431, +1-502-825-9033 [Kunzell] Ekkehard K"unzell, Spiele mit PENTAKUBEN, 1995, 5th Edition, ISBN 3-9804560-5-6, 80 pages, Pentakubenspiele, E. K"unzell, Sch"onrathstr. 79, D-52066 Aachen, Germany [Sillke] Torsten Sillke, http://www.mathematik.uni-bielefeld.de/~sillke/problems.html There you should find this contest and the K"unzell names of the pentacubes. Good luck, Torsten Sillke. // 1999-03-04 -- mailto:Torsten.Sillke@uni-bielefeld.de http://www.mathematik.uni-bielefeld.de/~sillke/