Questions

If you want bonus points, make sure you address each side of this tricky two-part question. 

The first part is addressing how you make sure you greet each and every customer who enters the store, giving them personal attention.  

The second part is how you would actually greet them – what would you say to them? Would you alert them of your newest products, ask if they’re looking for anything in particular or need guidance while shopping, or alert them to who they can reach out to if they require any assistance in various departments?

From the hints,

Only two options for 1st and 2nd digits => 4,2 and 9,3 since it is single digits

Sum of second and third digit  = 10 

If 2 => 3rd digit = 8

If 3 => 3rd digit = 7

4th digit = 2nd digit + 1 => (2+1 =3) or (3+1 = 4)

Sum of all digits = 30

Let 5th digit be x

=> 1st possibility = 4 + 2 + 8 + 3 + x = 30 => x = 13 (Not possible since it has 2 digits)

=> 2nd possibility = 9 + 3 + 7 + 4 + x = 30 => x = 7

Therefore, the PIN is 93747 

Number of spectral lines from a state n to ground state is

                   n(n-1)/2 = 6

The logic in the given puzzle is 

4 + 4 = 4 * 4+1 = 4 * 5 = 20

5 + 5 = 5 * 5+1 = 5 * 6 = 30

6 + 6 = 6 * 6+1 = 6 * 7 = 42

7 + 7 = 7 * 7+1 = 7 * 8 = 56

Similarly

9 + 9 = 9 * 9+1 = 9 * 10 = 90.

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