January 2016 - Page 2

petrw1 · 2015-12-30, 21:56

Waiting to see if my name gets honorable mention...

LaurV · 2015-12-31, 04:29

Hm... What's wrong with CVT?

axn · 2015-12-31, 05:10

Quote:

Originally Posted by R. Gerbicz

Maybe it was a little unfortunate wording in the puzzle.

It would be good to get an explicit clarification on this. Because, there is no shortage of solutions if we allow non-integral values. I have a 66 and a 67 (and bucket load of smaller numbers) if we allow non-integers. And I haven't even spent much time searching. Maybe even something as high as 75 might be possible.

R. Gerbicz · 2015-12-31, 08:34

Quote:

Originally Posted by axn

Maybe even something as high as 75 might be possible.

108 is a trivial upper bound.

CRGreathouse · 2016-01-04, 14:01

Quote:

Originally Posted by R. Gerbicz

108 is a trivial upper bound.

107 is a slightly less trivial bound: getting 108 requires hitting 15 primes (2, 5, 11, 17, 23, 29, 41, 47, 53, 59, 71, 83, 89, 101, 107), but hitting a prime requires that you have a prime in your original 12 numbers.

106 can also be achieved: the only way to hit 12 or fewer primes is to start at 1 and move up by 3 each time, but this requires having a 1 in each set which limits your primes to 10 tops.

I'm sure better bounds are not hard to come by (in the integer case, of course).

petrw1 · 2016-01-06, 17:21

Quote:

Originally Posted by petrw1

Waiting to see if my name gets honorable mention...

Yup....

R. Gerbicz · 2016-02-04, 17:00

The official solution is out: https://www.research.ibm.com/haifa/p...nuary2016.html

[..]
"A larger N can be achieved by 'cheating' and using non-integer numbers. For example,
S1={1,2,3,3.5,4,4.5} S2={2,6,12,13,14,15,16.5} yields 68."

That is not a solution. S2 has got 7 terms.

My own record submitted solution was for N=67:
S_1={1,5,6,7,8,9};
S_2={2,4,13/3,20/3,7,22/3};

(in the original problem this solution would earn for me eleven stars!)

2015-12-31, 04:29	#13
LaurV Romulan Interpreter Jun 2011 Thailand 9611₁₀ Posts	Hm... What's wrong with CVT? Last fiddled with by LaurV on 2015-12-31 at 04:30 Reason: link

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
January 2018	Xyzzy	Puzzles	0	2018-01-02 03:09
January 2017	Xyzzy	Puzzles	4	2017-02-22 21:34
January 2015	Xyzzy	Puzzles	1	2015-02-02 17:17
January 2008 Status	Wacky	NFSNET Discussion	0	2008-01-14 00:33
Records in January	wblipp	ElevenSmooth	10	2004-03-22 01:26

2015-12-30, 21:56	#12
petrw1 1976 Toyota Corona years forever! "Wayne" Nov 2006 Saskatchewan, Canada 2²·7·167 Posts	Waiting to see if my name gets honorable mention...

2016-02-04, 17:00	#18
R. Gerbicz "Robert Gerbicz" Oct 2005 Hungary 2²·7·53 Posts	The official solution is out: https://www.research.ibm.com/haifa/p...nuary2016.html [..] "A larger N can be achieved by 'cheating' and using non-integer numbers. For example, S1={1,2,3,3.5,4,4.5} S2={2,6,12,13,14,15,16.5} yields 68." That is not a solution. S2 has got 7 terms. My own record submitted solution was for N=67: S_1={1,5,6,7,8,9}; S_2={2,4,13/3,20/3,7,22/3}; (in the original problem this solution would earn for me eleven stars!)