5. Five young men, David, Juraj, Miha, Petar, and Matija, are spending their summer in Poreč, Primošten, Biograd, Šibenik, and Vrsar. They also have summer hobbies: swimming, cycling, speed walking, diving, and running. Discover which of them is spending the summer in which city and what hobby they are engaged in, given the following:

- David cycles, but not in Biograd, Šibenik, and Poreč.
- Juraj is not spending the summer in Šibenik.
- Miha is not spending the summer in Poreč and does not like speed walking.
- Matija has been diving all summer.
- The one who is spending the summer in Vrsar has been speed walking all summer.
- Petar is not spending the summer in Biograd, Primošten, and Poreč. He does not like speed walking and swimming.

Each task is scored with 10 points.

The use of a pocket calculator or any reference materials is not allowed.

NATIONAL COMPETITION IN MATHEMATICS
Opatija, March 31 - April 2, 2011.
5. 

|  | BI | VR | PR | PO | ŠI | pli | jed | hod | ron | bic |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| David | - | - | + | - | - | - | - | - | - | + |
| Matija | - | - | - | + | - | - | - | - | + | - |
| Juraj | - | + | - | - | - | - | - | + | - | - |
| Miha | + | - | - | - | - | + | - | - | - | - |
| Petar | - | - | - | - | + | - | + | - | - | - |
| pli | + | - | - | - | - |  |  |  |  |  |
| jed | - | - | - | - | + |  |  |  |  |  |
| hod | - | + | - | - | - |  |  |  |  |  |
| ron | - | - | - | + | - |  |  |  |  |  |
| bic | - | - | + | - | - |  |  |  |  |  |
|  |  |  |  |  |  |  |  |  |  |  |

David rides a bicycle in Primošten, Matija swims in Poreč, Juraj walks fast in Vrsar, Miha swims in Biograd, and Petar rows in Šibenik.

## NATIONAL MATHEMATICS COMPETITION

Opatija, March 31 - April 2, 2011.