A Long Row of Dice
Problem 641
Consider a row of dice all showing 1.
First turn every second die,, so that the number showing is increased by 1. Then turn every third die. The sixth die will now show a 3. Then turn every fourth die and so on until every th die (only the last die) is turned. If the die to be turned is showing a 6 then it is changed to show a 1.
Let be the number of dice that are showing a 1 when the process finishes. You are given and .
Find .