Great Pagoda (Japanese Crystal)

Designer : Unknown.

Great Pagoda 3

A		B		C

Pieces	3
Length	6
Goal	6×6×6
Holes	1
Solutions	0 / 2	without rotation
	1 / 2	with rotation
Moves	2

Great Pagoda 9

A		B..F	×5

G H	×2	I

Pieces	9
Length	6, 10
Goal	10×10×10
Holes	3
Solutions	0 / 12	without rotation
	5 / 12	with rotation
Moves	2

Great Pagoda 19

A		B..J	×9

K L	×2	M..P	×4

Q R	×2	S

Pieces	19
Length	6, 10, 14
Goal	14×14×14
Holes	3
Solutions	0 / 240	without rotation
	60 / 240	with rotation
Moves	2

Great Pagoda 33

A		B..N	×13

O..R	×4	S..X	×6

a b	×2	c..f	×4

g h	×2	i

Pieces	33
Length	6, 10, 14, 18
Goal	18×18×18
Holes	3
Solutions	0 / 5,376	without rotation
	960 / 5,376	with rotation
Moves	2

×17

×4

×10

×2

×2

×6

×2

×4

×2

Pieces	51
Length	6, 10, 14, 18, 22
Goal	22×22×22
Holes	3

Puzzles Old & New

A		P0
P1		P2
K2		K1

The number of pieces required in order to construct is as follows.

Pieces			1	2	3	4	5	6	7	8	9	10	11	12	13	N
Length			3	9	19	33	51	73	99	129	163	201	243	289	339	2N²+1
	4N+2	K1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
	4N+2	K2	1	2	2	2	2	2	2	2	2	2	2	2	2	2	: N≥2
1	6	A	1	1	1	1	1	1	1	1	1	1	1	1	1	1
1	6	P0		5	9	13	17	21	25	29	33	37	41	45	49	4(N−1)+1	: N≥2
2	10	P0			4	6	10	14	18	22	26	30	34	38	42	4(N−2)−2	: N≥4
2	10	P1			2	4	4	4	4	4	4	4	4	4	4	4	: N≥4
3	14	P0				4	6	10	14	18	22	26	30	34	38	4(N−3)−2	: N≥5
		P1				2	2	2	2	2	2	2	2	2	2	2	: N≥4
		P2					2	2	2	2	2	2	2	2	2	2	: N≥5
4	18	P0					4	6	10	14	18	22	26	30	34	4(N−4)−2	: N≥6
		P1					2	2	2	2	2	2	2	2	2	2	: N≥5
		P2						2	2	2	2	2	2	2	2	2	: N≥6
5	22	P0						4	6	10	14	18	22	26	30	4(N−5)−2	: N≥7
		P1						2	2	2	2	2	2	2	2	2	: N≥6
		P2							2	2	2	2	2	2	2	2	: N≥7
6	26	P0							4	6	10	14	18	22	26	4(N−6)−2	: N≥8
		P1							2	2	2	2	2	2	2	2	: N≥7
		P2								2	2	2	2	2	2	2	: N≥8
7	30	P0								4	6	10	14	18	22	4(N−7)−2	: N≥9
		P1								2	2	2	2	2	2	2	: N≥8
		P2									2	2	2	2	2	2	: N≥9
8	34	P0									4	6	10	14	18	4(N−8)−2	: N≥10
		P1									2	2	2	2	2	2	: N≥9
		P2										2	2	2	2	2	: N≥10
9	38	P0										4	6	10	14	4(N−9)−2	: N≥11
		P1										2	2	2	2	2	: N≥10
		P2											2	2	2	2	: N≥11
10	42	P0											4	6	10	4(N−10)−2	: N≥12
		P1											2	2	2	2	: N≥11
		P2												2	2	2	: N≥12
11	46	P0												4	6	4(N−11)−2	: N≥13
		P1												2	2	2	: N≥12
		P2													2	2	: N≥13
12	50	P0													4	4(N−12)−2	: N≥14
		P1													2	2	: N≥13
		P2														2	: N≥14
L	4L+2	P0														4(N−L)−2	: N≥L+2
		P1														2	: N≥L+1
		P2														2	: N≥L+2

Apr 29, 2004 by k16@chiba.email.ne.jp