Day Number

The day number is the serial number of the day in the relevant month (i.e., the number on 5 August 2016 is 5). The digit sum of the day is the sum of the values of all digits on the date of that day (i.e., the digit sum on 5 August 2016 is 5 + 8 + 2 + 0 + 1 + 6 = 22). A lucky day is one whose day number is equal to the digit of the day. Determine how many happy days there are in 2016 and which they are.

Final Answer:

n =  10

Step-by-step explanation:

$$\begin{gathered} 20.9.2016;2+0+9+2+0+1+6=20 \\ 21.9.2016;2+1+9+2+0+1+6=21 \\ 22.9.2016;2+2+9+2+0+1+6=22 \\ 23.9.2016;2+3+9+2+0+1+6=23 \\ 24.9.2016;2+4+9+2+0+1+6=24 \\ 25.9.2016;2+5+9+2+0+1+6=25 \\ 26.9.2016;2+6+9+2+0+1+6=26 \\ 27.9.2016;2+7+9+2+0+1+6=27 \\ 28.9.2016;2+8+9+2+0+1+6=28 \\ 29.9.2016;2+9+9+2+0+1+6=29 \\ n=10 \end{gathered}$$

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