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 2016-03-14, 16:35 #1 richs     "Rich" Aug 2002 Benicia, California 22×7×41 Posts Pizza Hut Meth Contest Win pizza for 3.14 years: 1. I’m thinking of a ten-digit integer whose digits are all distinct. It happens that the number formed by the first n of them is divisible by n for each n from 1 to 10. What is my number? 2. Our school’s puzzle-club meets in one of the schoolrooms every Friday after school. Last Friday, one of the members said, “I’ve hidden a list of numbers in this envelope that add up to the number of this room.” A girl said, “That’s obviously not enough information to determine the number of the room. If you told us the number of numbers in the envelope and their product, would that be enough to work them all out?” He (after scribbling for some time): “No.” She (after scribbling for some more time): “well, at least I’ve worked out their product.” What is the number of the school room we meet in?” 3. My key-rings are metal circles of diameter about two inches. They are all linked together in a strange jumble, so that try as I might, I can’t tell any pair from any other pair. However, I can tell some triple from other triples, even though I’ve never been able to distinguish left from right. What are the possible numbers of key-rings in this jumble?
 2016-03-14, 16:41 #2 Dubslow Basketry That Evening!     "Bunslow the Bold" Jun 2011 40
2016-03-15, 04:36   #3
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

17×113 Posts

Quote:
 Originally Posted by richs Win pizza for 3.14 years: 1. I’m thinking of a ten-digit integer whose digits are all distinct. It happens that the number formed by the first n of them is divisible by n for each n from 1 to 10. What is my number?
Here is 1 answer, I am sure there are others:

9216543870

Last fiddled with by a1call on 2016-03-15 at 04:39

2016-03-15, 07:50   #4
axn

Jun 2003

470810 Posts

Quote:
 Originally Posted by a1call Here is 1 answer, I am sure there are others: 9216543870
92165438 is not divisible by 8

There is only one solution, and is of the format OEOE5EOE0, which means you have to brute force 4!*4! = 576 permutations.

2016-03-15, 09:15   #5
0PolarBearsHere

Oct 2015

2×7×19 Posts

Quote:
 Originally Posted by axn 92165438 is not divisible by 8 There is only one solution, and is of the format OEOE5EOE0, which means you have to brute force 4!*4! = 576 permutations.
Well...
OEOE5EOEO0
But yes, 4!*4!

2016-03-15, 09:41   #6
axn

Jun 2003

22·11·107 Posts

Quote:
 Originally Posted by 0PolarBearsHere Well... OEOE5EOEO0

2016-03-15, 11:10   #7
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

36018 Posts

Quote:
 Originally Posted by axn 92165438 is not divisible by 8 There is only one solution, and is of the format OEOE5EOE0, which means you have to brute force 4!*4! = 576 permutations.
Excel roundung and late night calculations again,

3816547290

I verified with iPhone calculator.
Thanks for the reply and checking,

 2016-03-15, 16:11 #8 WMHalsdorf     Feb 2005 Bristol, CT 33×19 Posts For the first problem a for a brute force you would need to check if the number is a multiples of 2520 (the least common multipler of 1 thru 9).
2016-03-15, 17:41   #9
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

17×113 Posts

Quote:
 Originally Posted by WMHalsdorf For the first problem a for a brute force you would need to check if the number is a multiples of 2520 (the least common multipler of 1 thru 9).
3816547290 is not a multiple of 2520, yet it satisfies the constraints of the puzzle.

2016-03-15, 18:59   #10
WMHalsdorf

Feb 2005
Bristol, CT

33×19 Posts

Quote:
 Originally Posted by a1call 3816547290 is not a multiple of 2520, yet it satisfies the constraints of the puzzle.
3816547290 is not divisible by 7

1234759680 meets all constraints. Note there may be larger numbers.

2016-03-15, 19:02   #11
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

8,369 Posts

Quote:
 Originally Posted by WMHalsdorf 3816547290 is not divisible by 7 1234759680 meets all constraints. Note there may be larger numbers.

for the first thing only the first 7 digits need to be admittedly they aren't either but it's a key distinction. no your answer doesn't a number ending in 7 does not divide by 5. look at the new post a1call made it seems i was confusing your new number and their old one.

Last fiddled with by science_man_88 on 2016-03-15 at 19:24

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