Unlocking the Mystery of Flavius Josephus' Position in the Circle
Explore the intriguing historical puzzle of Flavius Josephus and his soldiers standing in a circle, determined by a unique pattern of self-sacrifice. Discover the systematic approach and mathematical thinking needed to reveal the safe position in the circle as the soldiers take turns wielding a sword in a grim ritual. Unravel the mystery and find the key to Josephus' strategic placement among his men in this ancient tale of survival.
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Presentation Transcript
Skills Skills Processes Processes 1. Simplify Be Systematic Be Organised 2. Record 3. Patterns
The story Flavius Josephus was a Jewish man who live about 2000 years ago One day his home town of Yodfat was under attack from the Roman army. Josephus led his army in a brutal, bloody battle, however he was clearly outnumbered and knew defeat was inevitable. He tried escaping, but the Romans had blocked all exits. Josephus and his men knew the Romans wouldn t accept their surrender, and there was only one thing left to do. They would have to kill themselves. But they couldn t face killing themselves, so they decide to do it together.
Josephus and his men stood in a circle and decided they would take it in turns to pick up the sword and kill the person next to them The 1st soldier picked up the sword and killed the 2nd 10 9 1 8 The 3rd then picked up the sword and killed the 4th 2 7 3 The 5th then picked up the sword and killed the 6th 6 F. F. J J 5 4 5 And so on until there was only one man left. Flavius Josephus Where was he standing?
In fact Flavius Josephus had 40 other soldiers with him, but he still knew the correct place to stand. 1 2 40 41 3 39 38 4 37 5 36 6 35 7 34 8 33 9 How could he know? 32 10 31 11 Is there a pattern for any number of people? 30 12 29 13 28 14 27 15 26 16 25 17 24 18 23 19 22 21 20
In fact Flavius Josephus had 40 other soldiers with him, but he still knew the correct place to stand. 1 2 40 41 3 39 38 4 37 5 36 6 35 7 34 Remember what we talked about before 8 33 9 Are you being systematic? 32 10 Have you organised your results? 31 11 Have you made and tested predictions 30 12 29 13 28 14 27 15 26 16 25 17 24 18 23 19 22 21 20
What have you noticed? Number of people Safe Position 2 3 4 5 6 7 8 9 10 11 1 3 1 3 5 7 1 3 5 7
What have you noticed? Number of people Safe Position 2 3 4 5 6 7 8 9 10 11 1 3 1 3 5 7 1 3 5 7
The rules Powers of 2 reset (the first person is safe) (2, 4, 8, 16, 32 etc ) You count up in odd numbers until you reach the next reset http://alejandroerickson.com/joomla/flash
