Midas Touch
The legendary King Midas possessed a huge amount of gold. He hid this treasure carefully in a building consisting of rooms. In each room there were a number of boxes; this number was equal to the number of rooms in the building. Each box contained a number of golden coins that equalled the number of boxes per room. When the King died, 1 box was given to the royal barber. the remainder of coins should be divided fairly between his sons. What is the max number of sons he can have?
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1 solution
Assume the number of rooms to be x+1 Then the number of boxes in each room will also be x+1 and the number of coins in each box will also be x+1 After 1 box has been given to the royal barber, x number of rooms will have x+1 boxes and 1 room will have x boxes. Therefore, the total number of coins would be x(x+1)(x+1) + x(x+1) x(x+1)(x+1) + x(x+1) = x(x+1)[(x+1) + 1] = x(x+1)(x+2)
Sice there were x+1 number of rooms, the maximum number of sons he can have will be The number of rooms + 1