|Spoiler Inside: Solution to Puzzle||SelectShow>|
The solution by one submitter (lightly edited):
“The father got none, so we can work backwards starting with 0.
The last son left 0. This is after taking an extra 2. Thus, when he took half, he left just two slices. Meaning he started with double that amount, 4 slices.
The second son thus left 4 slices at the end. This is after taking an extra 2 slices meaning there were 6 left after he took one-third. Thus, he started with 9.
The first son thus left 9 slices. This is after taking an extra 3. Thus, he left 12 after taking his quarter. Thus, 16 slices were there at the start.”