Twentieth Century Standard Puzzle Book / Three Parts in One Volume

by Unknown

No. LII.—A TRANSFORMATION

The flat-headed 3 can be turned into a 5 by one continuous line, without scratching out any portion of the 3, by treating the flat top of the 3 as part of a square drawn round the 5, thus:—

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No. LIII.—A CLEAR COURSE

Here is a list of ninety-two positions, in which eight pieces can be placed upon the chess or draughtboard so that each has a clear course in every direction.

1	1586	3724	24	3681	5724	47	5146	8273	70	6318	5247
2	1683	7425	25	3682	4175	48	5184	2736	71	6357	1428
3	1746	8253	26	3728	5146	49	5186	3724	72	6358	1427
4	1758	2463	27	3728	6415	50	5246	8317	73	6372	4815
5	2468	3175	28	3847	1625	51	5247	3861	74	6372	8514
6	2571	3864	29	4158	2736	52	5261	7483	75	6374	1825
7	2574	1863	30	4158	6372	53	5281	4736	76	6415	8273
8	2617	4835	31	4258	6137	54	5316	8247	77	6428	5713
9	2683	1475	32	4273	6815	55	5317	2864	78	6471	3528
10	2736	8514	33	4273	6851	56	5384	7162	79	6471	8253
11	2758	1463	34	4275	1863	57	5713	8642	80	6824	1753
12	2861	3574	35	4285	7136	58	5714	2863	81	7138	6425
13	3175	8246	36	4286	1357	59	5724	8136	82	7241	8536
14	3528	1746	37	4615	2837	60	5726	3148	83	7263	1485
15	3528	6471	38	4682	7135	61	5726	3184	84	7316	8524
16	3571	4286	39	4683	1752	62	5741	3862	85	7382	5164
17	3584	1726	40	4718	5263	63	5841	3627	86	7425	8136
18	3625	8174	41	4738	2516	64	5841	7263	87	7428	6135
19	3627	1485	42	4752	6138	65	6152	8374	88	7531	6824
20	3627	5184	43	4753	1682	66	6271	3584	89	8241	7536
21	3641	8572	44	4813	6275	67	6271	4853	90	8253	1746
22	3642	8571	45	4815	7263	68	6317	5824	91	8316	2574
23	3681	4752	46	4853	1726	69	6318	4275	92	8413	6275

The numbers indicate the position on the eight successive columns of the cells on which the men are to be placed. Of course, many similar arrangements arise from merely turning the board.

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No. LIV.—QUARRELSOME NEIGHBOURS