Calling to parents

Let us number the Sunday John first called his parent as day 1 or $d(1)=1$ . Then the number of days has lapsed when John made the $n$ th call is $d(n) = 3( n-1) + 1$ . Implying that $d(100)=298$ . To check which weekday was $d(100)$ , we find the remainder when it is divided by 7. $d(100) \bmod 7$ $= 298 \bmod 7 = 4$ . Since day 1 was Sunday, day 4 was Wednesday .

John calls his parents on the Sunday if the number of times he called is a multiple of 3. The larger multiple of 3 less than or equal to 100 is 99. So, on the 99 th time he calls it will be a Sunday. Therefore on the hundredth time he makes the call it will be Wednesday.