Saturday, January 17, 2009
Puzzle - Two in four and five
The puzzle:
On an impulse a man bought two large cans each full of oil at a bargain. Then, finding that they were too heavy for him, he engaged two helpers to carry them home for him, as he had figured out that after rewarding each a two liter portion it would still be advantageous for himself.
However when the helpers brought a four liter and a five liter container respectively he had a problem as there was no measuring utensils nor container available, except a small scoop. But being a thinking man he managed to apportion a two liter quantity in both the two containers, using the small scoop for transferring the oil, and all were happy as agreed.
How did he do it ?
The answer is below:
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
Nomenclature:
Let the cans be called Ca and Cb
and the helpers containers be called L4 and L5.
The procedure:
At start:
Ca = full, Cb = full, L4 = 0, L5 = 0
Fill L5 from Ca and then fill L4 from L5:
Ca = -5, Cb = full, L4 = 4, L5 = 1
Empty L4 into Ca and then empty L5 into L4:
Ca = -1, Cb = full, L4 = 1, L5 = 0
Fill L5 from Ca and then fill L4 from L5:
Ca = -6, Cb = full, L4 = 4, L5 = 2
Empty L4 into Ca and then fill L4 from Cb:
Ca = -2, Cb = -4, L4 = 4, L5 = 2
Fill Ca from L4 and it is done:
Ca = full, Cb = -4, L4 = 2, L5 = 2
QED:
On an impulse a man bought two large cans each full of oil at a bargain. Then, finding that they were too heavy for him, he engaged two helpers to carry them home for him, as he had figured out that after rewarding each a two liter portion it would still be advantageous for himself.
However when the helpers brought a four liter and a five liter container respectively he had a problem as there was no measuring utensils nor container available, except a small scoop. But being a thinking man he managed to apportion a two liter quantity in both the two containers, using the small scoop for transferring the oil, and all were happy as agreed.
How did he do it ?
The answer is below:
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
Nomenclature:
Let the cans be called Ca and Cb
and the helpers containers be called L4 and L5.
The procedure:
At start:
Ca = full, Cb = full, L4 = 0, L5 = 0
Fill L5 from Ca and then fill L4 from L5:
Ca = -5, Cb = full, L4 = 4, L5 = 1
Empty L4 into Ca and then empty L5 into L4:
Ca = -1, Cb = full, L4 = 1, L5 = 0
Fill L5 from Ca and then fill L4 from L5:
Ca = -6, Cb = full, L4 = 4, L5 = 2
Empty L4 into Ca and then fill L4 from Cb:
Ca = -2, Cb = -4, L4 = 4, L5 = 2
Fill Ca from L4 and it is done:
Ca = full, Cb = -4, L4 = 2, L5 = 2
QED:
# posted by chunmu @ 8:50 PM 
