Timeline for Does a 10-element set have 30 3-element subsets such that each pair is in two of these 30 subsets?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jun 19, 2012 at 16:32 | vote | accept | David Wasserman | ||
| Jun 18, 2012 at 22:27 | comment | added | Gerhard Paseman | If the poster cares to chew up computer cycles, here is one approach: find 10 vectors of length 30, each with entries either 0 or 1, such that each vector has exactly 9 occurrences of 1 and such that any two distinct vectors share exactly two coordinates with ones. A little reasoning allows you to assume the form of the first three vectors (possibly four) and the computer can check for the constraints on the remaining vectors. Gerhard "Ask Me About System Design" Paseman, 2012.06.18 | |
| Jun 18, 2012 at 21:44 | comment | added | Douglas Zare | In 394 of these, the designs are simple, which means the triples are distinct. A more natural interpretation of the question would be to add the condition that the block design is simple. | |
| Jun 18, 2012 at 21:32 | history | edited | Douglas Zare | CC BY-SA 3.0 |
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| Jun 18, 2012 at 21:24 | history | answered | Douglas Zare | CC BY-SA 3.0 |