Number of Chocolates in a Bag

April 11, 2023

Puzzle on Chocolates

This is a puzzle on the number of chocolates in a bag. Priyanka visited the “holy ghar,” a well-known monument which is situated near the Himalayas. It is a spherical building with a spiral stairway leading to the top.

Premise – From the summit, you can see the natural splendor that surrounds that location. Priyanka thought of reaching the top. She also brought a lot of chocolates for the youngsters.
Rules – As she climbs higher, chocolate falls from her purse with each step. When she reaches the summit, she gives half of the chocolates she has left to the tiny children. Chocolate slips down with each step in the process of climbing down. She repeats the ritual at five more holyghars, leaving her with no chocolates.
Objective – Can you figure out how many chocolates there were in total initially?

The solution to the Number of Chocolates in a bag

9300 chocolates are the answer. Let us see how to find the number of chocolates in a bag?

Let’s start at the beginning. First, we’ll look at the sixth holy ghar.

Priyanka descended a hundred steps, thus she must have been left with 100 chocolates after contributing.
She now provides half of the entire chocolates, implying that she had 200 chocolates before donating.
Now that she’s lost 100 chocolates while ascending, she’ll need 300 chocolates to reach the top of the fifth holy ghar.
The fourth holy ghar is now being treated in the same way.
So, before climbing fourth, she must have consumed (300+100)*2+100 chocolates, totaling 900.
She must have (900+100)*2 + 100, which equals 2100, before ascending third.
She must be eating 4500 chocolates right now before the rising second.

Finally, she must have 9300 chocolates before climbing. So she had a total of 9300 chocolates at the start.

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