Set during a war You will be captured along with 12 other people. They gather you all in a field and give you a gun and tell you to form a circle.

The rule of the game is simple; each in turn will kill the one to his left; This process continues until only one person is left. Which row of 1-13 you are in, are you last?

Let’s look at the scenarios first, starting with 2, thinking simple.

2: Person number one kills person number two, game over. Survivor: 1

3: Person number one kills person number two. Person number three kills person number one, game over: Survivor: 3

4: Person number one kills person number two. Number three kills number four. Number one kills number three: Survivor: 1

Going this way, the situation is up to 12:

A pattern emerges here. If noted, in circles of 2, 4, and 8, the number 1 always survives. All of these circles have personal numbers that can be expressed as powers of 2. In summary, if the number of people in the circle can be expressed with a value such as 2 to the n-th, it is necessary to take the number 1 rank.

But as we said in our question, if there’s a number that can’t be expressed as a power of 2, like 13. Which row should be chosen? Actually, the answer is very simple, you just need to find the largest number that comes before the number of people in the circle, which can be expressed as a power of 2. With 13 people this number is 8 (2 to 3).

Then we subtract this number from the number of people in the circle, and multiply the result by two, we add one. Good:

13-8=5
5×2=10
10+1=11

In summary, if there is a circle of 13 people, the person who is on the 11th row will be able to survive.

Let’s do another example, If there are 41 people in the circle, what order should you stand in? The largest number that comes before 41 and can be expressed as a power of 2 is 32 (2 to the 2).

41-32=9
9×2=18
18+1=19

Accordingly, the place where you should stand in the circle of 41 people is, 19th row.

Here’s the solution to this math game, just like this…