Question

1. Seven thieves try to share a hoard of gold bars equally between themselves. Unfortunately, six bars are left over, and in the fight over them, one thief is killed. The remaining six thieves, still unable to share (all) the bars equally since two are left over, again fight, and another is killed. When the remaining five share (all) the bars, one bar is left over, and it is only after yet another thief is killed that an equal sharing is possible. What is the minimum number of bars which allows this to happen? [Hint: Be carefully to check that the conditions for the Chinese Remainder Theorem apply before using it.]

Answer 1