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Posted on 2006-04-20

the date 8.8.64, meaning august 8,1964 is a very interesting date,because the product of the first 2 numbers equals the third.find the year of the twentieth century which gives the maximum dates of this kind.

8 Comments

factors for 24->1 2 3 4 6 8 12 24

1/24 2/12 3/8 4/6 6/4 8/3 12/2 --- 7 combos

Cheers!

Sunnycoder

my approach was to get factors for all numbers .. most of them can be eliminated easily ... some of them have upto 6 combos but advantage for 24 is that factors are small, so month and day can be interchanged ... e.g. 12/2 2/12

for larger factors, dates cannot work both ways since you have only 12 months ..

the year must be the product of the day and month, hence day and month combinations are like the prime factors of the "year".

the highest value of month is 12, which is 2*2*3, hence 3 factors. 8 = 2*2*2 has the same number of factors, but this gives only half of the possiblities because they are the sames.

The resulting year is hence a multiple of 12.

1912, 1924, 1936 ... etc

12 = 1*12, 2*6, 3*4, 4*3, 6*2, 12*1

24 = 2*12, 3*8, 4*6, 6*4, 8*3, 12*2, 24*1

36 = 3*12, 4*9, 6*6, 9*4, 12*3, 18*2

48 = 4*12, 6*8, 8*6, 12*4, 24*2

60 = 5*12, 6*10, 10*6, 12*5, 15*4, 20*3 (30*2 does NOT work :-)

72 = 6*12, 8*9, 9*8, 12*6

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