#math trivia #April4 solution

Burt Kaliski Jr. (@modulomathy)
4/4/12 7:14 PM
#math trivia for #April4: How many times this year do month and day both divide into year (’12)? In what year does this happen most often?

Another non-day-number problem, similar to #April3.

Both day and month divide into year 36 times in ’12: whenever both are among the six values 1, 2, 3, 4, 6 or 12.

Here, a very highly divisible number can be useful in any month whose number divides it. Larger years may seem better, but are not necessarily so. For instance, 96 is divisible by seven numbers between 1 and 12, as well as by 16 and 24, so the number of month/day combinations that works is 7*9 = 63. Meanwhile, 90 is divisible by seven numbers between 1 and 12, as well as by 15, 18, and 30, so yields 7*10-1 = 69 combinations (the omission being February 30). And 60 is divisible by eight numbers between 1 and 12 as well as 15 and 30, and thus produces 8*10-1 = 79 combinations, which is the record.

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