IBM Ponder This #118 · February 2008

The following integer sequences are the winning positions for a parametric two players game.

1. Find the rules of the game which are consistent with the partial data.
2. Fill in the missing values in the table according to those rules.

Parameter	Sequence
1	1	2	4	8	16	32	64	128	256	512	1024	2048	4096	8192	16384	...
2	1	2	3	5	8	13	21	34	55	89	144	233	377	610	987	...
2.5	1	2	3	5	7	10	15	22	32	47	69	101	148	217	318	...
3																...
3.5	1	2	3	4	6	8	11	15	21	27	35	46	61	82	109	...
4																...
4.5	1	2	3	4	5	7	9	11	14	18	22	27	34	43	54	...
5	1	2	3	4	5	6	8	10	12	15	18	22	27	33	41	...
5.5	1	2	3	4	5	6	8	10	12	15	18	22	26	31	37	...
6	1	2	3	4	5	6	7	9	11	13	16	19	23	27	32	...
6.5	1	2	3	4	5	6	7	9	11	13	15	18	21	25	29	...
7	1	2	3	4	5	6	7	8	10	12	14	16	19	22	26	...

Solution

Best opened after a real attempt

To be added.