On the fourth day of the year, 04/01/2021, the sum of the digits of the day and month was equal to the sum of the digits of the year. How many times will this happen in 2021?
Answers
51 patterns found for Monday, 4 January 2021.
Given : On the fourth day of the year, 04/01/2021, the sum of the digits of the day and month was equal to the sum of the digits of the year.
To Find : How many times will this happen in 2021
Solution:
04/01/2021
Day 04
Month 01
Sum of Digits of Day and Month = 0 + 4 + 0 + 1 = 5
Sum of digits of Year = 2 + 0 + 2 + 1 = 5
Sum of digits of Year = 5
Now for Jan Sum of Digits of month = 0 + 1 = 1
Sum of Digits of Day should be 5 - 1 = 4
04 , 13 , 22 , 31 ( 4 Days in January)
For Feb Sum of Digits of month = 0 + 2= 2
Sum of Digits of Day should be 5 - 2 = 3
03 , 12 , 21 ( 3 Days in February)
For Mar Sum of Digits of month = 0 + 3= 3
Sum of Digits of Day should be 5 - 3 = 2
02 , 11 , 20 ( 3 Days in March)
For Apr Sum of Digits of month = 0 + 4= 4
Sum of Digits of Day should be 5 - 4 = 1
01 , 10 ( 2 Days in April)
May , Jun , July , Aug , Sep has sum of Digit 5 or more hence no possible combination
After That Month of Oct Sum of Digits of month = 1 + 0 = 1
Sum of Digits of Day should be 5 - 1 = 4
04 , 13 , 22 , 31 ( 4 Days in October)
For Nov Sum of Digits of month = 1 + 1= 2
Sum of Digits of Day should be 5 - 2 = 3
03 , 12 , 21 , 30 ( 3 Days in November)
For Dec Sum of Digits of month = 1 + 2 = 3
Sum of Digits of Day should be 5 - 3 = 2
02 , 11 , 20 ( 3 Days in Dec)
4 + 3 + 3 + 2 + 4 + 4 + 3 = 23
23 times this will happen in 2021
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