**Hard Mathematical Logic Puzzle - 21 May**

A devotee visits 9 temples when he visits India. All these nine temples have one thing in common - there are 100 steps in every temple. The devotee puts Re.1 coin after climbing up every step. He does the same while climbing down every step. At each temple, the devotee offers half of his money from his pocket to god. In this way, his pocket becomes empty after his visit to 9th temple.

Can you calculate the total amount he had initially ?

**For Solution :**Click Here

He originally had 51100 coins.

ReplyDelete127700 ... presumably sacrifice to god takes place at top of stairs

ReplyDelete1,27,700/-

ReplyDeletei lakh what you did there anonymous ;)

ReplyDelete146900

ReplyDeleteIn such cases, we calculate from the last thing. Thus in this case, let us start counting from the 9th temple. Since, he must have offered 100 coins while climbing down stairs, it means that he must have offered Rs. 100 to god on the ninth temple and offered Rs. 100 while climbing up steps. Thus it is clear that he had Rs. 300 in his pocket before climbing the steps of the 9th temple.

Similarly, we will calculate for all the temples backwards.

Before eight temple: (300+100)*2 + 100 = 900

Before seventh temple: (900+100)*2 + 100 = 2100

Before Sixth temple: (2100+100)*2 + 100 = 4300

Before fifth temple: (4300+100)*2 + 100 = 8900

Before fourth temple: (8900+100)*2 + 100 = 18100

Before third temple: (18100+100)*2 + 100 = 36,500

Before second temple: (36500+100)*2 + 100 = 73300

Before first temple: (73300+100)*2 + 100 = 146900

Therefore he had Rs. 146900 initially.

but (2100+100)*2 + 100 is not equal to 4300

Delete=(2100+100)(2) + 100

=(2200)(2) + 100

=4400 + 100

=4500

your math is wrong .... (2100+100)*2 = 4400

ReplyDeleteCorrect Answer Is 153300.... Check from reverse order....

ReplyDelete153300.... by thi

ReplyDelete153300

ReplyDeleteIf we start from the end,

ReplyDeleteConsider we start out at the last temple with amount x,

=> x - (100 + (x-100)/2 + 100) = 0

i.e., total coins now - (100 while going up + half of left to god + 100 going down) will be equal to 0.

Solving this,

=> (x-300)/2 = 0

i,e, x = 300 for the 9th temple.

Now, notice that the value 0 of right hand side(RHS) can be replaced with 300 to calculate x (or total coins on starting at temple 8)

i.e., => (x-300)/2 = 300 to get x = 900...

and so on...

Just replace the value on the R.H.S and calculate the starting coins for any temple.