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### Hard Mathematical Logic Puzzle

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 ?

1. He originally had 51100 coins.

2. 127700 ... presumably sacrifice to god takes place at top of stairs

3. 1,27,700/-

4. i lakh what you did there anonymous ;)

5. 146900

In 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.

1. but (2100+100)*2 + 100 is not equal to 4300
=(2100+100)(2) + 100
=(2200)(2) + 100
=4400 + 100
=4500

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

7. Correct Answer Is 153300.... Check from reverse order....

8. 153300.... by thi

9. If we start from the end,

Consider 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.