100 People in a Circle Puzzle Help

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100 People in a Circle Puzzle Help

Postby millie9 » Wed Aug 01, 2018 10:02 am

Hi,

I need help in solving the following puzzle from this website

Code: Select all
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?


Answer is integer.
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Re: 100 People in a Circle Puzzle Help

Postby creint » Wed Aug 01, 2018 4:12 pm

Checked with excel and code and found a solution.
Spoiler:
Hidden Text: Show
It's 73 probably.
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Re: 100 People in a Circle Puzzle Help

Postby millie9 » Thu Aug 02, 2018 6:36 am

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



Thanks. The answer is correct.

Can you pls explain your though process behind the answer. As still I've no clue how is the given number is correct.
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Re: 100 People in a Circle Puzzle Help

Postby 1to9only » Thu Aug 02, 2018 1:23 pm

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.
Code: Select all
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.
Code: Select all
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
Code: Select all
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
Code: Select all
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
Code: Select all
9 25 41 57 73 89 [9]
s k  s  k  s  k   s

Round 6, 3 in circle
Code: Select all
9 41 73 [9]
s k  s   k

Survivor:
Code: Select all
73
s

s=sword, k=killed
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Re: 100 People in a Circle Puzzle Help

Postby tarek » Fri Aug 03, 2018 4:51 pm

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
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Re: 100 People in a Circle Puzzle Help

Postby tarek » Fri Aug 03, 2018 5:30 pm

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

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