Timeline for Picking collections to get over half the number of each type of object
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 19, 2010 at 2:30 | comment | added | Aaron Meyerowitz | I don't see that mixing objects or having more than one object in a box always makes it easier. We start with n boxes and $n_1$ objects of type 1 spread between them. Clearly we take take the $\lfloor \frac{n+1}{2} \rfloor$ fullest boxes and have more than half the type 1 items. Now spread $n_2$ type 2 objects in the same boxes. Why is it obvious that we can use $\lfloor \frac{n+2}{2} \rfloor$ boxes, still have at least half the type 1 objects but also have at least half the type 2 objects? Maybe a fruitful question is How many ways are there to choose $\frac{n+k}{2}$ boxes so that... | |
| Aug 18, 2010 at 15:06 | comment | added | Hugh Thomas | @Casebah-- but if boxes contain more than one item, that only makes it easier to get all the items you need. | |
| Aug 17, 2010 at 7:43 | comment | added | Casebash | The boxes may contain mixed types - ie. a box may have an apple and an orange | |
| Aug 17, 2010 at 7:15 | history | answered | Artem Kaznatcheev | CC BY-SA 2.5 |