a date to reckon with

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.
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1924 has 7 such dates
shilpi84Author Commented:
how do we figure this out?
Hi shilpi84,

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

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oops I posted too late ...

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 ..
Guy Hengel [angelIII / a3]Billing EngineerCommented:
by "design"...
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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shilpi84Author Commented:
i m still not able 2 understand that y we always check 4 multiples of 12.:((
We don't have to always check for multiples of 12
30 = 1*30, 2*15, 3*10, 5*6, 6*5, 10*3
but that's only six dates of this kind, which is not as many as seven for
24 = 2*12, 3*8, 4*6, 6*4, 8*3, 12*2, 24*1
Guy Hengel [angelIII / a3]Billing EngineerCommented:
I don't think that accepting only my comment is fair, as ozo and sunnycoder posted the same value earlier...
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