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, 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.