Formation of Brahmins and thieves
The Story
A group of 15 learned Brahmins were travelling through a forest. They were attacked by 15 thieves. At the same time a demon also appeared there. All the 30 men were terrified at the sight of the demon. But the leader of the learned Brahmins thought of a plan to save his followers and made a pact with the thieves and the demon to sacrifice 15 of the 30 men.
All the 30 men would stand in a circle with positions numbered 1 to 30. The demon would begin the count with the person in the position numbered 1 and eat the 10th living person and from there it would continue to count and eat the next 10th person making rounds along the circle. This was to continue until the demon would have eaten 15 people in all.
The leader of the learned Brahmins chanted a mantra before the exercise began.
ईक्षण कुकालं महाभूतांतकम् । यमयुगसोमं नायकरामम् ॥
हिमांशुनयनं नासत्य रूपम् । बुधोक्त मर्मं तस्कर कर्मम् ॥
The thieves thought that to be a prayer. The number of safe positions and the positions where one was certain to die were alternately represented using the Bhūtasaṃkhyā system in the above verse. Knowing the positions where one was safe and where one would die, the learned Brahmins sneaked into the safe positions. All the thieves were eaten by the demon and all the 15 learned Brahmins continued with their journey.
Table showing the safe and unsafe positions.
Applet to study the outcomes when the count 10 in this story is changed to other numbers between 1 and 30.
Comments
This is a problem related to the arrangement of objects in a circle as in the famous
Josephus problem.