- Math »
- There is a pond in front of a temple. in the pond 1st day 1 one flower was there, On 2nd day 2 flowers were there, on 3rd day 4 flowers came, on 4th day 8 flowers came.

# There is a pond in front of a temple. in the pond 1st day 1 one flower was there, On 2nd day 2 flowers were there, on 3rd day 4 flowers came, on 4th day 8 flowers came.

Step into the tranquil scenery of a temple pond where flowers multiply exponentially each day. Curious about when the pond reaches half its capacity? Explore the intriguing calculation!

by Maivizhi A

**Updated **Mar 18, 2024

## There is a pond in front of a temple. in the pond 1st day 1 one flower was there, On 2nd day 2 flowers were there, on 3rd day 4 flowers came, on 4th day 8 flowers came, on 5th day 16 flowers came, and so on. On 30th day pond is filled with flowers. How many days it would have taken to fill half of the pond with flowers?

It would take **29 days** to fill half of the pond with flowers.

Here's the reasoning:

- The number of flowers doubles each day, following a geometric progression.
- We need to find the day (d) when the number of flowers (a) is half of the total number of flowers on the 30th day (a_total). We can express this as a fraction: a = a_total / 2.
- Since the number of flowers doubles every day, we can represent the number of flowers on day d as a = 1 * 2^(d-1), where 1 is the initial number of flowers on day 1.
- Substituting into the first equation, we get: 1 * 2^(d-1) = (a_total) / 2.
- To solve for d, we can rewrite the equation as 2^(d-1) = (a_total) / 2. Since the pond is full on the 30th day, a_total must be the number of flowers that grow on the 30th day, which is double the number of flowers that grow on the 29th day.
- Therefore, (a_total) / 2 is the number of flowers that grow on the 29th day.
- Plugging this back into the equation, we get: 2^(d-1) = 2^(29-1).
- Solving for d, we find that d = 29.

Therefore, it takes **29 days** for the number of flowers to reach half of the total number of flowers on the 30th day, meaning the pond is half full on the 29th day.

## What is Cardinality of Sets?

Cardinality is a concept in set theory that refers to the "size" or "number of elements" in a set. It provides a way to compare the sizes of sets, even if the elements themselves are different. For finite sets, the cardinality is simply the count of elements in the set.

For example:

- The set {1, 2, 3} has a cardinality of 3 because it contains three elements.
- The set {apple, orange, banana} also has a cardinality of 3, despite containing different types of elements (fruits instead of numbers).

For infinite sets, such as the set of all natural numbers or the set of all real numbers, cardinality becomes a bit more complex. In these cases, different types of infinity are used to denote the size of the set, such as countable infinity or uncountable infinity.

Cardinality is denoted using the symbol "|A|", where A is the set, and |A| represents the cardinality of set A.

## There is a pond in front of a temple. in the pond 1st day 1 one flower was there, On 2nd day 2 flowers were there, on 3rd day 4 flowers came... - FAQs

1. What is the pattern of flower growth in the pond?

The number of flowers in the pond doubles each day, following a geometric progression.

2. How many flowers are there on the 30th day?

The pond is filled with flowers on the 30th day.

3. When was the first day that the pond had more than one flower?

The second day is the first day the pond had more than one flower.

## Recent Updates

- Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevati...
- Yuto and Lian are at train stations 1,880 kilometers apart. Yuto boards a train heading...
- Aman’s salary is first increased by 25% and then decreased by 20%. The result is the ...
- P and S can complete a piece of work in 20 and 15 days respectively. They worked togeth...
- Each day that a library book is kept past its due date, a $0.30 fee is charged at midni...
- Teri goes shopping for some new clothes and then out to lunch with a friend. She spends...
- Two pipes A and B can fill a tank is 8 minutes and 14 minutes respectively. If both the...
- A and B stand at distinct points of a circular race track of length 135 m. They cycle a...
- The image of a candle flame placed at a distance of 30 cm from a mirror is formed on a ...
- In pea plants, Tall plant height is dominant over short plant height. If there are 200 ...
- A wall of length 10 m was to be built across an open ground. The height of the wall is ...
- A company contracts to paint 3 houses. Mr. Brown can paint a house in 6 days while Mr. ...
- In a forest 20% of Mushrooms are Red, 50% Brown and 30% White. A Red mushroom is poison...
- In a large population, 76% of the households own microwaves. A simple random sample of ...
- A bag contains 8 red marbles, 9 yellow marbles, 7 green marbles. How many additional re...