Solution:

To find out the day of the birthday of the third child, we need to first determine the day on which 20th December falls.

Step 1: Finding the Day of the Week for 20th December

We can use any of the standard methods to find the day of the week for a given date. Here, we will use the Doomsday rule, which is based on the fact that certain dates in each year always fall on the same day of the week. The Doomsday for any given year is the day of the week that falls on the same date in each of the 12 months of the year. For example, the Doomsday for the year 2021 is Sunday, since 4/4, 6/6, 8/8, 10/10, 12/12, and many other dates fall on a Sunday in 2021.

To find the day of the week for 20th December, we can use the Doomsday for the year 2021, which is Sunday. We know that 4/4 is a Doomsday, and that it falls on a Sunday in 2021. Therefore, we can determine the number of days between 4/4 and 20/12 as follows:

April (month of 4/4) has 30 days, so we add 26 days to get to the last day of April (4/30).
May (next month) has 31 days, so we add 31 days to get to the last day of May (5/31).
June has 30 days, so we add 30 days to get to the last day of June (6/30).
July has 31 days, so we add 31 days to get to the last day of July (7/31).
August has 31 days, so we add 31 days to get to the last day of August (8/31).
September has 30 days, so we add 30 days to get to the last day of September (9/30).
October has 31 days, so we add 31 days to get to the last day of October (10/31).
November has 30 days, so we add 30 days to get to the last day of November (11/30).
December has 20 days, so we add 20 days to get to 20/12.
The total number of days is 242, which is divisible by 7 with a remainder of 2. This means that 20/12 is two days after the Doomsday (Sunday) for 2021, which is Tuesday.

Therefore, the birthday of the third child falls on a day that is two days after Tuesday, which is Thursday.

Step 2: Finding the Days of the Week for the Birthdays of the First Two Children

We are given that the first child's birthday falls on the 5th Monday of April. This means that the first Monday of April is the 5th day of April, and the first child's birthday is 4/5. We can use the same method as above to find the day of the week for 4/5, which is Monday.

Similarly, we are given that the second child's birthday falls on the 5th Thursday of November. This means that the first Thursday of November is the 5th day of November, and the

D- November month is 30 days
So 30-5=25
Dec is 20
25+20=45
45/7=3 is the remainder
Friday, Saturday and Sunday
So Sunday is the Ens