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Australian AMC 2013 - Junior Question 27

AMC AUSTRALIA · Australian AMC 2013 - Junior

Question 27

Whenever Callum reads a date like 1/8/2013, he incorrectly interprets it as two divisions, with the second one evaluated before the first one:

$$1\div(8\div2013)=251\frac58.$$

For some dates, like this one, he does not get an integer, while for others, like 28/7/2013, he gets $28\div(7\div2013)=8052$, an integer. How many dates this year (day/month/year) give him an integer?