(1..100).each do |n|
	@cards=Array.new(n){|i| i+1}

	while @cards.size!=1
		@cards.push(@cards.shift)
		@cards.shift
	end

	puts "#{n}: #{@cards[0]}"
end

1: 1
2: 1
3: 3
4: 1
5: 3
6: 5
7: 7
8: 1
9: 3
10: 5
11: 7
12: 9
13: 11
14: 13
15: 15
16: 1
17: 3
18: 5
19: 7
20: 9
21: 11
22: 13
23: 15
24: 17
25: 19
26: 21
27: 23
28: 25
29: 27
30: 29
31: 31
32: 1
33: 3
34: 5
35: 7
36: 9
37: 11
38: 13
39: 15
40: 17
41: 19
42: 21
43: 23
44: 25
45: 27
46: 29
47: 31
48: 33
49: 35
50: 37
51: 39
52: 41
53: 43
54: 45
55: 47
56: 49
57: 51
58: 53
59: 55
60: 57
61: 59
62: 61
63: 63
64: 1
65: 3
66: 5
67: 7
68: 9
69: 11
70: 13
71: 15
72: 17
73: 19
74: 21
75: 23
76: 25
77: 27
78: 29
79: 31
80: 33
81: 35
82: 37
83: 39
84: 41
85: 43
86: 45
87: 47
88: 49
89: 51
90: 53
91: 55
92: 57
93: 59
94: 61
95: 63
96: 65
97: 67
98: 69
99: 71
100: 73