# Quod Erat Demonstrandum

## 2008/07/13

### 組合小談

Filed under: Additional / Applied Mathematics,HKALE,Pure Mathematics — johnmayhk @ 2:11 下午
Tags:

(i) $X$ 的每一對元素（即二元子集）恰巧在一個 $A_i$ ($1 \le i \le m$) 中；
(ii) $A_1, A_2, ..., A_m$ 中每兩個恰巧有一個公共元。

## 3 則迴響 »

Label the students as 1,2,…,30
On the first night, 16-30 stay at home, 1,2,3,…,15 visit everyone of 16-30.
After this night, each one of {1,2,..,15} and {16,..,30} have visited each other.
We use similar method for the two disjoint subsets {1,2,..,15} and {16,…,30} now. e.g. 8-15, 23-30 stays at home, 1-7 visit 8-15, 16-22 visit 23-30.
Repeat. In this way, students will visit 15 ppl on the first day, 8 ppl on the second, 4 on the third, 2 on the fourth. After 4 days they would have visited all other 29 students.

迴響 由 Soarer — 2008/07/15 @ 4:54 下午 | 回應

2. 謝謝 Soarer。原題指的互訪，是 A 到 B 的（比方說）宿舍探訪後，B 也要往 A 宿舍探訪他。但 Soarer 指出的更合符現實。

迴響 由 johnmayhk — 2008/07/15 @ 8:00 下午 | 回應

3. “是 A 到 B 的（比方說）宿舍探訪後，B 也要往 A 宿舍探訪他"

I see, no wonder I found “7 nights" weird.

迴響 由 Soarer — 2008/07/17 @ 1:31 上午 | 回應