Just Move Them

Logic Level 3

There are 3 boxes $A$ , $B$ , and $C$ . Initially, box $A$ has 8 balls but $B$ and $C$ are empty. Chris wants box $C$ to have as many balls as possible. He can do so by moving some balls from a box to another with the constraint that he can only move exactly $i$ balls on the $i^{\text{th}}$ step.

What is the maximum possible number of balls box $C$ can have?

5 6 7 8

1 solution

Christopher Boo
Aug 30, 2016

I created a table to keep track of balls in each steps

A	B	C
8	0	0
7	1	0
5	3	0
5	0	3
1	0	7
6	0	2
0	0	8

Hence the answer is 8.

We could also only involve boxes $A$ and $C$ , with the steps being

$(A,C) = (8,0), (7,1), (5,3), (2,6), (6,2), (1,7), (7,1), (0,8)$ ,

which involves $7$ steps as opposed to your $6$ -step process. A bonus here is that on the next step, the $8$ th, we can move $8$ balls from $C$ to $B$ , so that on the same sequence we can have each of the boxes having $8$ balls at some point in the sequence.

Brian Charlesworth - 4 years, 9 months ago

How do you generalize this?

Agnishom Chattopadhyay - 4 years, 9 months ago

Just Move Them

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