Balti Tee 1995 · Ülesanne 12
Kombinatoorika
Assume we have 95 boxes and 19 balls distributed in these boxes in an arbitrary manner. We take six new balls at a time and place them in six of the boxes, one ball in each of the six. Can we, by repeating this process a suitable number of times, achieve a situation in which each of the 95 boxes contains an equal number of balls?
Kui oled valmis
Ülevaatematerjal muutub kättesaadavaks järgmise päevaülesannete komplektiga.
Ülevaade
Teemad
Mängud ja strateegiad · Algoritmid ja protsessid · Induktsioon ja rekursioon
Lahendused
Lahendus
Solution:
Since , we can put times balls in the boxes so that the number of balls in one of the boxes increases by two, while in all other boxes it increases by one. Repeating this procedure, we can either diminish the difference between the number of balls in the box which has most balls and the number of balls in the box with the least number of balls, or diminish the number of boxes having the least number of balls, until all boxes have the same number of balls.
Võistluse kontekst
Balti Tee tulemused 1995
9 võistkonda
- Keskmine tulemus
- 3,9 / 5
- 4 või 5 punkti
- 6 / 9
- Eesti
- 4 / 5
Punktijaotus
Kõigi võistkondade punktid
| Võistkond | Punktid |
|---|---|
| Poland | 5 / 5 |
| Latvia | 5 / 5 |
| Sweden | 5 / 5 |
| Lithuania | 3 / 5 |
| Denmark | 4 / 5 |
| Finland | 5 / 5 |
| St. Petersburg | 1 / 5 |
| Estonia | 4 / 5 |
| Iceland | 3 / 5 |