Monday, June 27, 2005

 

Problem# 8

Two beggars A and B managed to get a 13-litres-jar full of Vodaka . They have two more jars of 5 and 10 litres respectively. They decided to divide the amount equally, with the aid of the jars and leave the undivided amount for a third beggar C, who was near by. What's the maximum amount the beggars A and B can have, if they are to use only the jars available with them to make the division? Also show the steps to make the division.

Hint: Is it possible to make a division (6 + 6 + 1)?

Comments:
6+6+1 division is not possible.
They will divide it as 5+5+3.

division is easy:
5 10 Jar
---------
E E 13
5 E 8
E 5 8
5 5 3

E- Empty
 
Well, that's good! But, why is
6 + 6 + 1
not possible? Any explanations?

ANOTHER VERSION:
-----------------
What's the maximum amount the beggar C can get, if he were allowed to make the partition (such that each beggar gets a non-zero amount)?

How does he make the partition?
 
The maximum amount begger C can get is 3.

There is no other partition possible other than 5+5+3.

This is because size of 2nd jar - 10 is multiple of 5 which is the size of another jar.
 
The maximum amount begger C can get is 3.

There is no other partition possible other than 5+5+3.

This is because size of 2nd jar - 10 is multiple of 5 which is the size of another jar.
 
OK, that's an acceptable reason.
 
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