Musings over the Magical Temple Puzzle (4 minutes read)

Yesterday, someone posted this puzzle in our apartment whatsapp group.  It goes like this.  

A man starts from his house with some money to visit four temples.

1. As soon as he enters temple 1 his money gets doubled. He donates Rs 100 and moves.

2. At temple 2, again his money is doubled and he donates Rs 100

3. His money is doubled again at temple 3 and once again he donates Rs 100.

4. At temple 4 again his money gets doubled. He donates Rs 100 again and returns home empty handed.

How much money he had when he started from his house???

By the time I saw the message, a few of them had already responded with their solutions.  I was thrilled to take it up as a challenge.

In schooldays, Algebra used to be a fascinating subject for me.  My mind immediately started to decipher the puzzle and structured it in form of an Algebraic model.

My mind started calculating that assuming I had Rs x at beginning, it became 2x as I entered Temple 1 and on exit become 2x-100.  When I entered Temple 2 it became 4x-200 and on exit 4x-300.  Similarly,in Temple 3 it became 8x-600 on entry and 8x-700 on exit.  It Temple 4 it became 16x-1400 on entry and 16x-1500 on exit. Since I was left with No money at end, it can be expressed in form of an equation as 16x-1500=0 or 16x=1500 or x=1500/16 or x=Rs 93.75

I immediately cross-checked my answer with what others had posted and was happy to have got it right. 

At that time, I was wondering how others would have approached this problem? Do all humans perceive problems and situations in a uniform manner?  Is there only one way to deal with the problem?

The algebraic model that I applied follows a top-to-down approach i.e. looks at the problem at a comprehensive way, understands each of the components and limitations of the system, which will become a driving force to reach the end goal.

I asked myself, what if someone had not studied Algebra? Can they not solve the problem?

One alternate approach to problem solving is to remain focussed on the end goal that you want to achieve and work backwards to figure out, what would be the immediate preceding step I should be in that will help me reach the goal in the next step.  Instead of finding out a solution that will help us reach our goal, we can visualise the goal to help us to figure out the steps that lead to the goal.

Let me explain.  In this context, I would start to visualise that if I had to be left with no money upon exit from temple 4, it means I should have exactly Rs 100 after I enter temple 4, which inturn means, I must have Rs 50 before I enter temple 4 (since money would double up upon entering the temple).

Stretching this visualisation further backwards, I should have had Rs 150 after entering temple 3 and Rs 75 just before I entered temple 3.

Similarly, I would have had Rs 175 after entering temple 2 and Rs 87.50 immediately before I entered temple 2. 

And finally, I would have had Rs 187.50 after entering temple 1 and concluded that I should have Rs 93.75 immediately before I entered temple 1. 

I am now left wondering how would a lay man who has neither studied algebra nor has the IQ to reverse-engineer the problem (as demonstrated above) would have handled the situation.

I could get reminded of this guy at the general provision store.  When I ask him for a kilogram of any grain, he dips his fist into the gunny bag to fetch the grain to the weighing scale and then repeats it 5 times.  Thereafter he reads the weight in the scale and then starts a sort of jugglery i.e. either adding some more grain bit by bit or reducing it bit by bit till the indicator stops at 1000 grams. 

To put the above analogy in perspective to the problem in our hand, I would first start with any number between Rs 50 and Rs 100 as a trial answer (because if I start with less than Rs 50 in hand, I would not have Rs 100 to donate during exit at temple 1 and if I have more than Rs 100 then my cash balance after exit from each temple would only grow positive and I can never remain with Nil cash at end of any temple exit).

So I start with a random Rs 80 at first and realise that I fall short by Rs 60 to donate in 3^rd temple. So I increase it another bit to say Rs 90 and then realise that I still fall short by Rs 60 to donate in the 4th temple. Now I beef up my guesstimate to Rs 95.  This time I realise that I am left with Rs 20 even after exit from the 4th temple.  I soon realise that my answer should therefore lie anywhere between Rs 90 and Rs 95.  I do some more iterations and after 5 to 6 attempts realise that my correct answer is Rs 93.75.

Such trial and error approach to problem solving does not guarantee any time frame in which you would get the desired results.  Further in real life, many a times we do not get enough time or enough resources to spend on trials. Sometimes the actions we do are irreversible and therefore take a huge risk if we adopt the trial and error approach.

I am sure there would be some more approaches to arrive at the solution, that what is discussed above.  

But what if someone could not think of any clue to solve the problem?   In real life as well, we come upon situations where in spite of our best efforts, we still cannot find ways to navigate through the problem. What should we do in such cases? 

Instead of complaining that we do not know how to overpower the problem, make an assessment of the damage that the problem can do to you and budget for the consequences in your mind.  Once you mind is prepared for the worst, you will be able to absorb the shock with grace and eventually come out of the storm in more dignified manner.  We would learn to accept and live with the problem.

Concluding lines....

Every problem can be solved in multiple ways, it all depends on how we choose to approach them.  

If we realise our strengths and limitations, we can channelise it to work for us to find the solutions.  

If you are not able to solve the problem, then first accept it and prepare yourself for the damage it can do to you.  You will come out of in a better manner.