# Question :

100 people standing in a circle in an order 1 to 100.

No.1 has a sword.

He kills next person (i.e. no. 2) and gives sword to next to next (i.e no.3).

All person does the same until only 1 survives.

Which number survives at the last?

# Solution :

• Round 1 : 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99
• Round 2: 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97
• Round 3: 1, 9, 17, 25, 33, 41, 49, 57, 65, 73, 81, 89, 97
• Round 4: 9, 25, 41, 57, 73, 89
• Round 5: 9, 41, 73
• Round 6: 9, 73
• Round 7: 73

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