Answer:
Son number 1 has 3 full, 5 half, and 3 empty barrels.
Son number 2 has 4 full, 3 half and 4 empty barrels.
Son number 3 has 3 full, 5 half, and 3 empty barrels.
Step-by-step explanation:
Let's first calculate the amount of honey we have (in barrel unit):
10*1 + 13*0.5 + 10*0 = 16.5 honey units
As the father wants to split it equally between the 3 sons, each of them should get 16.5 / 3 = 5.5 honey units
And since we have 33 barrels in total which must be split equally between the sons, each should receive 33 / 3 = 11 barrels.
Since the sons are identical, let's start by splitting each of the barrels equally. We can rearrange later to match all criteria:
3 full, 4 half, and 3 empty for each of the sons, makes it 10 barrels and 3*1 + 4*0.5 + 3*0 = 5 honey unit
For 3 sons there would be 1 full, 1 half and 1 empty barrels left
We can give 1 half barrel to the 1st son, now he has 11 barrels and 5.5 units of honey. He's good to go. we have 1 full, 1 and 1 empty barrels left.
Give the full barrel to the 2nd son, now he has 11 barrels, but 6 unit of honey. So we trade the empty barrel for a half barrel of his. So he would have 4 full, 3 half and 4 empty barrels. That accounts for 11 barrels, 4*1 + 3*0.5 + 3*0 = 5.5 barrels.
We are left with 1 half barrel, that can be given to the 3rd son, now he would have 3 full, 5 half, and 3 empty barrels. That accounts for 11 barrels and 3*1 + 5*0.5 + 3*0 = 5.5 unit of honey.
