July 2013
We are sorry to disappoint those of you who expected to see an elegant solution, but we don't know of one for this version of the Golomb ruler problem.
If you find one - please send it to us and we'll publish it.
There are many ways to solve this month's challenge - mostly just using computerized calculations to search for possible solutions.
The only (up to a symmetrical) solution is 1, 3, 6, 35, 75, 108, 121, 130.
Many of you solved a greedy version of the problem (see sequence A096772 in The On-Line Encyclopedia of Integer Sequences) and got the wrong solution: 1, 2, 5, 14, 33, 72, 125, 219.
Some of you solved the more general problems for sets of nine and ten integers:
1, 2, 18, 27, 128, 139, 186, 205, 209
1, 7, 11, 35, 112, 131, 235, 268, 299, 310
John Tromp also submitted his solution to the OEIS as sequence A227358. Thank you, John, for sharing your results and for holding the publication till the end of the month.
If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com