My thousands digit is the first that is perfect.but if you're not happy with that,it's also the product of the first two primes,according to my precocious cat.
My units digit is the odd of those primes,and if you look at it and my tens,you'll find a number divisible by three,but not by the square of that,friends.
Now let's look at my hundreds and thousands.If you examine those two as they're paired,you'll find they form a divisible by an even prime that's been squared.
Now let's look at my body in whole.Five different dights you see,in order (or not) you'll find that they are divisible by nine,yes siree!
Can you find the mystery number?
2006-08-30
15:32:59
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14 answers
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asked by
Hyun-Joong Kim
2
in
Science & Mathematics
➔ Mathematics
6093
The first perfect number is 6 (= 2x3 = 1+2+3).
The units digit is a three.
There are two possibilities for the tens place:
3 and 9 because 33 and 93 are divisible by three but not nine.
There are three possibilities for the hundreds place:
0,4,8 because 60,64 and 68 are divisible by 4.
The only combination of the tens and hundreds place digits given above that leads to a number evenly divisible by nine
is 6093/9=677.
P.S. I assume you meant 4 digits in the last clue line, because otherwise the number is not unique, as 66033, 56493 and 16893 all fit the bill.
2006-08-30 15:43:28
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answer #1
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answered by 1,1,2,3,3,4, 5,5,6,6,6, 8,8,8,10 6
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Thousands digit = 2 x 3 = 6
Odd one of these is 3, and a two-digit number ending in 3, divisible by 3 but not by 9 must be 33 or 93, but later the verse says the digits are all different so it must be 93.
So we now have 6 _ 9 3
Then we're told that 6 _ is divisible by 4, so it must be 60 or 64 or 68.
Next comes the surprise info that there's a fifth digit, and that the number is (presumably; not, as stated, "the digits are") divisible by 9. Since 6, 9 and 3 total 18, the other two digits must total 9 to keep the total of all digits divisible by 9. There are two possibilities:
56493 and 16893.
2006-08-30 22:50:21
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answer #2
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answered by Hy 7
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wild guess:
26451....
your first clue should have been ten thousandth.... and the first two primes are 2 and 1 they're product = 2
2 _ _ _ _
units digit, odd of those primes meaning 1
2_ _ _ 1
looking at the tens (combining it with the 1) should be divisible by 3 but not of its square... therefore either 21 or 51... but later you commented 5 different digits, since there's a two... go with 51
2 _ _ 51
hundreds and thousands = divisible by and even prime (2 being the only even prime) that's been squared meaning 4, going with all being different only number that can be use is 64...
26451 (divisible by 9: final clue)
26451 / 9 = 2939
thus the answer is 26451... = )
now, do i get my ten points?....
2006-08-30 22:55:08
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answer #3
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answered by VeRDuGo 5
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6 is the thousands
3 is the units
9 in the tenths
thats all that i can say for sure, the hundreds can be 0 4 or 8 becuase 60 64 68 are all divisible by 4.
if it is 0 then the tenthousands must be a multiple of 3, if it is 4 the ten thousands will be a multiple of 3 plus 2 and if it is8 it will be a multiple of 3 plus 1
2006-08-30 22:47:17
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answer #4
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answered by locomexican89 3
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01621
by the way you said nothing about the ten thousand digit
2006-08-30 22:40:15
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answer #5
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answered by Serendipity 3
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6093, Matt is correct
2006-08-31 00:04:13
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answer #6
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answered by JustAnotherUser 1
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45063
2006-08-30 22:41:34
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answer #7
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answered by Keaman 2
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46233
2006-08-30 22:41:24
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answer #8
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answered by The Ry-Guy 5
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Fifteen?
2006-08-30 22:37:42
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answer #9
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answered by pacific_crush 3
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did u say it was a poem?
2006-08-30 22:38:36
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answer #10
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answered by cheenarca 3
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