20160314, 16:35  #1 
"Rich"
Aug 2002
Benicia, California
2^{2}×7×41 Posts 
Pizza Hut Meth Contest
Win pizza for 3.14 years:
1. I’m thinking of a tendigit 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 puzzleclub 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 keyrings 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 keyrings in this jumble? 
20160314, 16:41  #2 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
1C1D_{16} Posts 
1 is trivial to brute force.
2 reminds me of the similar problem about the Russian mathematician's sons' age. Presumably it's a similar sort of answer. I don't even understand 3. 
20160315, 04:36  #3  
"Rashid Naimi"
Oct 2015
Remote to Here/There
17×113 Posts 
Quote:
9216543870 Last fiddled with by a1call on 20160315 at 04:39 

20160315, 07:50  #4 
Jun 2003
4708_{10} Posts 

20160315, 09:15  #5 
Oct 2015
2×7×19 Posts 

20160315, 09:41  #6 
Jun 2003
2^{2}·11·107 Posts 

20160315, 11:10  #7  
"Rashid Naimi"
Oct 2015
Remote to Here/There
3601_{8} Posts 
Quote:
How about 3816547290 I verified with iPhone calculator. Thanks for the reply and checking, 

20160315, 16:11  #8 
Feb 2005
Bristol, CT
3^{3}×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).

20160315, 17:41  #9 
"Rashid Naimi"
Oct 2015
Remote to Here/There
17×113 Posts 

20160315, 18:59  #10 
Feb 2005
Bristol, CT
3^{3}×19 Posts 

20160315, 19:02  #11  
"Forget I exist"
Jul 2009
Dumbassville
8,369 Posts 
Quote:
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 20160315 at 19:24 

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