MathDB

Bucket

A

contains 3 litres of syrup. Bucket

B

contains

n

litres of water. Bucket

C

is empty. We can perform any combination of the following operations: - Pour away the entire amount in bucket

X

, - Pour the entire amount in bucket

X

into bucket

Y

, - Pour from bucket

X

into bucket

Y

until buckets

Y

and

Z

contain the same amount.
(a) How can we obtain 10 litres of 30% syrup if

n = 20

? (b) Determine all possible values of

n

for which the task in (a) is possible.

Problem Statement