Tower of Brahma

                                                                        Tower of Brahma

The Tower of Brahma (also called the Tower of Hanoi, indeed it is more widely known by this name, I’d imagine) is a puzzle that also offers a teaching/learning moment in schools and to first year engineering students (most puzzles do, and I am taking this as an example). 

Three circular discs with a hole at the centre are stacked on a pole per increasing diameter top down (smaller at the top, if anyone has any doubts). There is also a set of three poles and the discs can slide down the poles. Let us call the pole on which the discs are stacked on the “original” pole (How original, eh?), in the figure above, the left most. 

The task is to move all the three discs from the “original” to any one of the other two poles, on the condition that at no time a larger disc can be on top of a smaller disc. What is the minimum number of moves needed to achiever the target? I am not giving the solution as it is well known.

Have our students learned anything beyond solving this puzzle? I seriously doubt that.

Just suppose one student asks herself, “OK, I have solved this puzzle, it is so simple. The answer I get cannot be any smaller, as any move at any step besides the one I made will violate the condition. Hence, I am right. Voila!” 

But, as studious as she is, “What if there are four discs?” she asks. Not one to ask for help, she follows all the rules and gets the correct sequence of the moves with the appropriate disc. In fact she sees that, after getting three discs in order, she has to move the fourth disc and go through one more stacking of three disks. That is, shifting three discs directly indicates the number of moves involving four discs. None of the three discs on the move are smaller than the fourth. “I am OK!” 

The fifth comes along, and she knows that she is on the right rack and does not do the shifting and gives the response immediately!

The student is better than smart, she is brilliant. She decides to check whether she can do the same with the reverse order of discs, with the appropriately changed condition, a smaller disc cannot be placed on a bigger disc; it has to be the other way, after all from the original puzzle. She learns one more thing: to test whether something is equivalent to some other thing, one has to accommodate ALL the rules and regulations in both the cases.

Just one puzzle enabled the student to learn so much!

Obviously Lord Brahma thought of that as after creating all the beings and their souls. He had time one hand. While Yahweh rests on the seventh day, Brahma indulges Himself playing this game/puzzle! We are so superior, of course!

Raghuram Ekambaram