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# a date to reckon with

Posted on 2006-04-20
Medium Priority
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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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Question by:shilpi84
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LVL 85

Expert Comment

ID: 16504705
1924 has 7 such dates
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Author Comment

ID: 16504713
how do we figure this out?
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LVL 45

Expert Comment

ID: 16504727
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

Cheers!
Sunnycoder
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LVL 45

Expert Comment

ID: 16504735
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 ..
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LVL 143

Accepted Solution

Guy Hengel [angelIII / a3] earned 1000 total points
ID: 16504738
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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Author Comment

ID: 16504793
i m still not able 2 understand that y we always check 4 multiples of 12.:((
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LVL 85

Expert Comment

ID: 16504885
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
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LVL 143

Expert Comment

ID: 16506352
I don't think that accepting only my comment is fair, as ozo and sunnycoder posted the same value earlier...
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