[Guest]

Suppose there are some 10 men standing in a circular ring.Name them 1 to 10 in order.

Now the first man is given a knife.He passes the knife to the man who is next to him in the ring.

Now the man with the knife kills the man next to him and gives the knife to the next person alive.

(i.e. 4th in this case since 3rd one is killed).Now 4th one passes the knife to fifth one who kills

6th and gives the knife to the 7th man.And so the sequence is continued...

See....

initial: 1 2 3 4 5 6 7 8 9 10

After first round of killing: 1 2 4 5 7 8 10 .....(3,6 & 9 been killed)

At the end of round one No.9 has just been killed and no.10 has the knife.

No.10 will give the knife to 1 who'll kill 2 and hand over the knife to 4...

And the sequence continues.....(i.e. after an kill knife is passed two times before the next kill...)

After Round 2: 1 4 5 8 10

After Round 3: 4 5 10

After Round 4: 4 10

After Round 5: "4"

So No.4 Will be the Last Man Standing!

So who'll be alive in the end if the ring consisted of i)100 men.

ii)1000 men.

Is there anyway to represent the answer by mathematical expression?

[superprismatic]

Let the function LMS(n) be the number of the last man standing when we start with n men.

i) LMS(100)=91

ii) LMS(1000)=604

In general, For n=1, we have LMS(1)=1 and for n>1, we have LMS(n) = ((LMS(n-1)+2) mod n)+1.

[wolfgang]

Suppose there are some 10 men standing in a circular ring.Name them 1 to 10 in order.

Now the first man is given a knife.He passes the knife to the man who is next to him in the ring.

Now the man with the knife kills the man next to him and gives the knife to the next person alive.

(i.e. 4th in this case since 3rd one is killed).Now 4th one passes the knife to fifth one who kills

6th and gives the knife to the 7th man.And so the sequence is continued...

See....

initial: 1 2 3 4 5 6 7 8 9 10

After first round of killing: 1 2 4 5 7 8 10 .....(3,6 & 9 been killed)

At the end of round one No.9 has just been killed and no.10 has the knife.

No.10 will give the knife to 1 who'll kill 2 and hand over the knife to 4...

And the sequence continues.....(i.e. after an kill knife is passed two times before the next kill...)

After Round 2: 1 4 5 8 10

After Round 3: 4 5 10

After Round 4: 4 10

After Round 5: "4"

So No.4 Will be the Last Man Standing!

So who'll be alive in the end if the ring consisted of i)100 men.

ii)1000 men.

Is there anyway to represent the answer by mathematical expression?

The last standing man will be number 91( if we begin with No. 1).

[Guest]

@Superprismatic:Thanks for ur insight and contribution