MathDB

A shop sells bottles with this capacity:

1L, 2L, 3L,..., 1996L

, the prices of bottles satifies this

2

conditions:

1

. Two bottles have the same price, if and only if, your capacities satifies

m - n = 1000

2

. The price of bottle

m

(

1001>m>0

) is

1996 - m

dollars. Find all pair(s)

m

and

n

such that: a)

m + n = 1000

b) the cost is smallest possible!!! c) with the pair, the shop can measure

k

liters, with

0<k<1996

(for all

k

integer) Note: The operations to measure are: i) To fill or empty any one of two bottles ii)Pass water of a bottle for other bottle We can measure

k

liters when the capacity of one bottle plus the capacity of other bottle is equal to

k

3