Minimum Spans in Difference Triangles

The table below gives the smallest known spans for various size difference triangles. It was last updated on February 3, 2003.

How are we doing? If these spans had been entered in the Triangles Programming Contest, Wayne's winning entry would have scored only 23.75 points instead of 23.96. A theoretical entry, made up of the best triangles submitted to the contest, would have scored 23.79 points against the triangles above.

Here's how to update this table:

Send an email to alzimmerma@aol.com with just the word TRIANGLES in the subject line.

Each email can contain as many triangles as you like. Here's an example of the body of an email containing two triangles:

6, 1, 10, 8; Yes; John Smith;
Exhaustive

88, 941, 262, 1210, 1159, 62, 1194, 1203,
42, 1184, 1221, 40, 1185, 1129, 1, 1125,
1127, 6, 1176, 1155, 78, 1112, 827, 701,
327; Unknown; Ringo Starr; Drummer's Heuristic

There are four fields separated by semicolons: Sequence, Optimal, Submitter and Method. All but Sequence are free-form text fields and can contain anything.

The information for a triangle can be spread across multiple lines, and you can leave blank lines between triangles for readability. Note that you can only put a line break after a comma or a semicolon. If your email software automatically inserts line breaks in long lines then you should insert the line breaks yourself to ensure that they occur at acceptable places (that is, after commas and semicolons).

When I receive an email I'll convert the sequences to canonical form and add them to a local database. I'll then regenerate this page from the database.

I will not send out acknowledgments, either positive or negative. If you send triangles and they don't appear here within 24 hours, check your email for errors and resend. If all else fails, let me know that you're having a problem.

Al Zimmermann