Question 25
Whenever Sam reads a date like 20/11/2016, he incorrectly interprets it as two divisions, with the second one being evaluated first before the first one. For example,
$$20\div(11\div2016)=\frac{40320}{11}=3665\frac5{11}.$$
For some dates, like the example above, he does not get an integer result, while for some, like for 20/8/2016, he gets $20\div(8\div2016)=5040$, which is an integer. How many dates this year (day/month/year) will give him a non-integer answer?
$$20\div(11\div2016)=\frac{40320}{11}=3665\frac5{11}.$$
For some dates, like the example above, he does not get an integer result, while for some, like for 20/8/2016, he gets $20\div(8\div2016)=5040$, which is an integer. How many dates this year (day/month/year) will give him a non-integer answer?