Josephus Problem: 100 Soldiers in a Circle Riddle
A popular riddle which you should attempt if you have never came across it.
100 Soldiers are 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 the soldiers do the same until only 1 survives.
Which number will survive at the end?
So were you able to solve the riddle? Leave your answers in the comment section below.
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Answer:
The straight forward way of solving this qould be manually writing down 1 to 100 and then striking out the numbers as per the problem.
In such a scenario it would go like this;
Round 1: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99
Round 2: 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
Round 3: 1, 9, 17, 25, 33, 41, 49, 57, 65, 73, 81, 89, 97
Round 4: 9, 25, 41, 57, 73, 89
Round 5: 9, 41, 73
Round 6: 9, 73
Round 7: 73
so answer is 73
what if their were 1000 soldiers??
would it be possible to solve it by this method??
Yes but it would consume a lot of time.
Here’s the correct way of solving this riddle.
This is actually a classic Josephus Problem.
The original Josephus Problem goes like this;
“The problem is named after Flavius Josephus, a Jewish historian living in the 1st century. According to Josephus’ account of the siege of Yodfat, he and his 40 soldiers were trapped in a cave, the exit of which was blocked by Romans. They chose suicide over capture and decided that they would form a circle and start killing themselves using a step of three. Josephus states that by luck or possibly by the hand of God, he and another man remained the last and gave up to the Romans.”
Solution to the Riddle using Josephus Problem approach:
The solution requires getting the nearest smaller number that is the power of 2, in this case 64 and subtract it with the given number.100-64=36.
Now we apply the formula;
2n+1 = 2*36 + 1 = 72 + 1 = 73.
Hence answer = 73