The remainder when N is divided by 18 is 16, translated :

N=18k+16\frac{N}{4} is divided by 18 means what is the remainder of

\frac{N}{4*18}?

Given that N is a multiple of 28, translated:

N=28m\frac{N}{4*18} with

N=28m is

\frac{28m}{4*18} or

\frac{7m}{18} and its "form" can be written as

7m=18q+R ( or 14m=36q+2R, this will be useful later)

Going back to the first equation

N=18k+16 =

28m=18k+16 =

14m=9k+8. From the equation before is its "useful" form 14m=36q+2R

so puttin them together

9k+8=36q+2R all the numbers k,q,R must be integer 8-2R=36q-9kif q and r are 0

8-2R=0 so

R=4 value #1the other possible value of R (because must be positive, it's a reminder) will be in the case 9k>36q

The difference

36q-9k can be (36-45) = -9 but

8-2R=-9 means R=17/2 no integer

difference -18 => R = 5

value #2difference -27 => R = 33/2 no integer

difference -36 => R=21 out of range 0,18

We can stop here bigger differences mean R out of 0,18 range

2 values,

B(I am not sure of my method though, the Master Mind could help here and +1 to the question! it took me 10 minutes to came up with a solution!)

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