Number of Chocolates in a Bag
Puzzle on Chocolates
This is a puzzle on 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 splendour 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, a chocolate falls from her purse with each step. When she reaches the summit, she gives half of the chocolates she has left to tiny children. A 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?
Solution to Number of Chocolates in a bag
9300 chocolates is 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 rising second.
Finally, she must have 9300 chocolates prior to climbing. So she had a total of 9300 chocolates at the start.
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