## 100 People in a Circle Puzzle Help

For fans of all other kinds of logic puzzles

### 100 People in a Circle Puzzle Help

Hi,

I need help in solving the following puzzle from this website

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`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?`

millie9

Posts: 2
Joined: 01 August 2018

### Re: 100 People in a Circle Puzzle Help

Checked with excel and code and found a solution.
Spoiler:
Hidden Text: Show
It's 73 probably.
creint

Posts: 230
Joined: 20 January 2018

### Re: 100 People in a Circle Puzzle Help

creint wrote:Checked with excel and code and found a solution.
Spoiler:
Hidden Text: Show
It's 73 probably.

Can you pls explain your though process behind the answer. As still I've no clue how is the given number is correct.
millie9

Posts: 2
Joined: 01 August 2018

### Re: 100 People in a Circle Puzzle Help

I found the survivor by this method (similar to pen and paper)!

Round 1, it helps to think of the 100 starters as paired, e.g. 1-2, 3-4 ... 99-100 - so 1 kills 2, 3 kills 4 ... 99 kills 100, and passes sword back to 1.
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`1 2 3 4 5 6 ... 94 95 96 97 98 99 100 [1]s k s k                   s  k  s  k   s`

Round 2, still an even number (50) in circle and paired, e.g. 1-3, 5-7 ... 97-99 - so 1 kills 3 ... 97 kills 99, and passes sword back to 1.
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`1 3 5 7 9 11 ... 87 89 91 93 95 97 99 [1]s k s k                   s  k  s  k   s`

Round 3, an odd number (25) in circle - so the 24th gets killed, the 25th gets the sword and kills number 1
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`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 [1 9]s k s k                                                        s  k  s   k s`

Round 4, 12 in circle
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`9 17 25 33 41 49 57 65 73 81 89 97 [9]s k  s  k              s  k  s  k   s`

Round 5, 6 in circle
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`9 25 41 57 73 89 [9]s k  s  k  s  k   s`

Round 6, 3 in circle
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`9 41 73 [9]s k  s   k`

Survivor:
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`73s`

s=sword, k=killed
1to9only

Posts: 2265
Joined: 04 April 2018

### Re: 100 People in a Circle Puzzle Help

There is a formula which escapes me now that tells the answer, and will also tell you the cycle the original ordinal and current ordinal

tarek

tarek

Posts: 3748
Joined: 05 January 2006

### Re: 100 People in a Circle Puzzle Help

Remembered it now:

If the number of people in the circle can be expressed as (2^p)+x then the surviving person will be 2x+1. Now we can safely go for a circle of 10,000

For a programming challenge:
1. Number of cycles
2. Number of people remaining after each cycle
3. Original person ordinal when cycle and current ordinal are known
4. During which cycle a certain person is going to die when his original ordinal is known

tarek

tarek

Posts: 3748
Joined: 05 January 2006