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The math exercise that will swell your head - but will save your life
A complex math exercise based on a historical event drives everyone crazy - when those who surrender to it complain about headaches and solve correctly for a super rewarding feeling.
Will you be able to surpass the method?
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Mathematics
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Friday, 10 April 2020, 00:09
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The video reveals the place from which the Romans broke through the walls of Jerusalem 2,000 years ago, as described in Joseph Bon Matityahu
's book This Is How Math Meets Suicide Squad: A complicated mathematical exercise that has existed since the days of the First Temple His.
The exercise is actually a riddle in combinatorics called the "Josephus Problem", named after Josephus Flavius (Yosef ben Matityahu) the Jewish historian.
The riddle is based on the event in which after the fall of Yodfat in 67 Josephus and another 40 Jewish warriors were captured in a cave by the Romans. His comrades chose to commit suicide and not fall captive. . In this way will not have anybody to kill himself and could not repent after the death of his friend. they formed a circle, so that each combatant party circuit commit suicide, to die everybody - except one will have to carry out suicide himself. very optimistic until now.
Josephus was not thrilled that doomed He had to die and was afraid to tell his friends about it. So he calculated where in the circle he should stand so that he would be the last to stay. For example, if Josephus was in a group of five people - he would have to stand in third place. So - by law - the first would kill the second, The third is the fourth, the fifth is the first and the third is the fifth - so the third remains last. In the case of Josephus they were 41 soldiers and in order to stay alive he had to stand in 19th place. How? this.
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To the full article
The video with the complete solution:
In the first round it is quite clear that anyone in the even number will die, so in order to survive you must settle in an odd number.
When the round ends, it starts from the beginning and your position in the order changes because the one in front of you and after you are no longer alive.
The next pattern that is easy to spot is that if the total number of soldiers is a power of 2 (1,2,4,8,16,32 and so on), then the right place for you is the 1st place.
Think about it: if there are two people - 1 kills 2. When there are four people in a circle - 1 kills 2, 3 kills 4 and 1 kills 3. No matter how high you go up to 2, always the first soldier is the one to start the round And that which will survive him.
But what do you do if it's not a power of 2?
Well it's already more complicated.
In such a case - the last survivor will be the one whose turn to kill will come when the number of people left is equal to a power of 2. For example - the initial number of people in Josephus' circle is 41, and the highest number of power 2 lower than 41 is 32 (2 to power 5).
It follows that there is a need for 32 people to still be alive when it is your turn to kill another person.
Arman explains that if every second person dies, you should be in a position that is twice the difference between 41 and 32 (9) - and another, Yosef ben Matityahu himself.
The equation for finding the winning position in this case is
19 = 1 + 9 * 2.
And Yosef ben Matityahu calculated all this in his head he was in position number 19 when the killing began.
By the way, in the end he stood last along with another person.
But because he did not want to die "nor to defile his hand with brotherly blood," he persuaded his friend not to commit suicide and to surrender to the Romans in order to save their lives.
He became a historian and his four books became one of the most important sources in Roman history.
Quiz: Are you an expert at reading body language?
What number do you see here?
Half of you will be wrong and big time
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