Question

Vikram has three boxes A, B, and C initially containing 0, 0, 27 balls respectively. He wants to get equal number of balls in each box but the constraint while doing the transfers is that at every i th move he has to transfer exactly i balls from one box to another. And he cannot transfer balls between A and B.
How many minimum steps( if possible) will you take to get to equal number of balls in each box?

• A. 7
• B. 8
• C. 9
• D. Not possible

Answer 1

The correct option is A 7

As per the given constraint we can only transfer i no. of balls in the i th transfer. Let’s see what this actually means. in the first step you can transfer exactly 1 ball (i=1) in the second step you can transfer exactly 2 balls (i=1) To ensure equal number of balls in all the three boxes, each box should have 9 balls.
$\begin{array}{cccc}StepDescription& A& B& C\\ InitialCondition& 0& 0& 27\\ Move1ballfromCtoAinStep1& 0+1& 0& 27-1=26\\ Move2ballsfromCtoBinStep2& 1& 0+2& 26-2=24\\ Move3ballsfromCtoAinStep3& 1+3=4& 2& 24-3=21\\ Move4ballsfromCtoAinStep4& 4+4=8& 2& 21-4=17\\ Move5ballsfromAtoCinStep5& 8-5=3& 2& 17+5=22\\ Move6ballsfromCtoAinStep6& 3+6=9& 2& 22-6=16\\ Move7ballsfromCtoBinStep7& 9& 2+7=9& 16-7=9\\ Final& 9& 9& 9\end{array}$
Hence it will take 7 transfers to get 9 balls in each box. All the transfers are demonstrated in the picture.