X + Y

laorenjia

昨晚一家去看了x + y (數造天才)，想在大銀幕看英國片同唔抗拒數學嘅(因數學内容要比 Imitation Game 或者講 game theory 始祖 John Nash 嘅 A Beautiful Mind 為多)，有孩子想參加 International Mathematical Olympiad 更應該看看。

睇到一半，妻子在我耳邊問我戲裏面講嗰啲數我識唔識得晒，我老實回報：你以為我係天才咩？妻子又趁機施展魔法：喺呀，我一路當你係天才㗎。我當然不是天才，但也確實看明了戲中教練要主角Nathan七步成詩般解答下面一個幾無聊又幾有趣的問題，讀完初中嘅細路應已具有解題所需知識：

枱面上放有一排二十張未打開嘅啤牌，隨意翻開一張後，隨即將該張啤牌右面的一張啤牌翻轉(turn over)。換言之，中途右面嗰張若已打開就要較要反轉番佢。唔駛講，亦唔可以揀最右嗰張嚟反，因右手面冇牌。

證明：無論你揀邊張反(開始或途中)，最後一定係所有牌都被翻開晒。

可以用五六張牌先試試。

dsedse

了解自閉症但有天才的心路歷程，體驗母愛的偉大

laorenjia

可以看看是否明白Nathan的解釋。

http://www.theguardian.com/film/video/2015/mar/04/x-and-y-clip-asa-butterfield-video?CMP=embed_video

shadeslayer

原帖由 laorenjia 於 15-03-25 發表
本帖最後由 laorenjia 於 15-3-25 11:58 編輯

昨晚一家去看了x + y (數造天才)，想在大銀幕看英國片同唔 ...

證明：無論你揀邊張反(開始或途中)，最後一定係所有牌都被翻開晒。

Xxxx
LRJ,

片中説的 terminate 和你的描述有點出入？

Nathan 個答案呀女話明，我唔知佢係未真係明。

laorenjia

shadeslayer 發表於 15-3-27 09:10
證明：無論你揀邊張反(開始或途中)，最後一定係所有牌都被翻開晒。

Xxxx

我係驚嗰教練講得太簡單啲人唔明，所以畫蛇添足加啲解釋，在揀牌打開其實可揀最右一張，但只不過右手邊冇牌俾你翻轉，有一可能到最後只剩下最右一張未打開，最後一個動作就係將佢打開而結束。
解決此題目需要一點二進制知識。1喺二進制都係1，2就係10，3就係11，由於3>2>1，所以喺二進制就係11>10>01，知道呢樣就好辦。

shadeslayer

原帖由 laorenjia 於 15-03-27 發表
我係驚嗰教練講得太簡單啲人唔明，所以畫蛇添足加啲解釋，在揀牌打開其實可揀最右一張，但只不過右手邊冇牌 ...

我覺得有出入的地方唔係最右一張牌，係只有第一張翻開的牌的右面會全翻開=must terminate. 第一張翻開的牌的左面不會全翻開。

Anyway, not important. My math phobic daughter seems to be interested in this movie after watching your movie clip. Thanks.

laorenjia

回覆 shadeslayer 的帖子

試吓用個四張牌簡單例子說明一下：

牌未打開用1代表，翻開後用0代表。

四張牌全未打開，即1111。假設我們翻開左手面數起第二張，同時亦反轉其右手面的牌，則1111就变成1001。這時我們可選擇打開的牌只有最左面和最右面的牌，假設我們打開最左面的牌，亦隨即反轉其右手面的牌，則1001就变成0101。假設我們這時打開左手數起第二隻牌，亦隨即反轉其右手面的牌，0101就变成0011。若我們再打開右手面數起第二張牌，再隨即將其右手面的牌反轉，所有牌就已經打開，0011就变成0000，遊戲結束。

如果你觀察數字的变化：
1111
1001
0101
0011
0000

你就會看到，呢個四位二進數字在每次動作後都會变小，所以变成0是一定的結果。

shadeslayer

原帖由 laorenjia 於 15-03-28 發表
本帖最後由 laorenjia 於 15-3-28 12:44 編輯

回覆 shadeslayer 的帖子

You are probably correct. I might have imposed myself nonexistent rule of not allowing to go back to the left of the first card picked by the player.

laorenjia

shadeslayer 發表於 15-3-28 13:44
You are probably correct. I might have imposed myself nonexistent rule of not allowing to go back to ...

妻子其實正式讀數比我多，當年曾考GCE A level的 higher maths, 女孩子中不常見。前一陣子妻子翻出大學時econometrics 的筆記，女兒才相信媽咪原來除咗購物折扣率外也曾讀過點其它數學。妻子在戲院中亦未聽明，故你女兒能看得明，是有點慧根了。

shadeslayer

原帖由 laorenjia 於 15-03-28 發表
本帖最後由 laorenjia 於 15-3-28 14:25 編輯

佢話咋，要最少打五折的。不過引起她興趣也不錯。

laorenjia

bladerunner 發表於 15-3-28 17:14
這條題目要明白Nathan解釋其實十分容易，初中生也絕對可以，但若要如片中Nathan般在那麼短時間就能想出個解 ...

I absolutely agree someone with an A in hkal pure maths should be able to understand the solution right away and coming up with the answer is a different matter.  However, according to a mathematical olympian, the question is entirely trivial and he also solved the question in a split second just like Nathan. I believed him. There are just geniuses like them around. I had the misfortune of knowing some of these people in my younger days. They completely dwarfed my childhood ambition to become a scientist (I had the misconception then you had to be really clever to become a scientist). Then I went astray into the business world.

laorenjia

bladerunner 發表於 15-3-29 20:00
你所講的那位mathematical olympiian 有可能真的是位天才（不過多數不是，因為叫得做天才的是極少數），而 ...

It depends in a way how you define a genius. Maybe you're using yourself as a yardstick and I'm using myself. My elder daughter's ex-boyfriend got A in both pure and applied maths in hkal but I honestly don't think he's the cleverer of the two. But when I compared my daughter to one of her classmates, my daughter almost looked like retarded. She went on to read quantitative finance at hku.

In general, people with IQ over 130 are called gifted, over 140 near genius, over 160 genius.With HK's average IQ close to 110 and a standard deviation of 15 or 16, there's no need for me to tell you there are thousands of such geniuses around us, although the relative percentage is small.

laorenjia

bladerunner 發表於 15-3-30 16:44
首先，天才與否不能憑考試成績來判斷，所以那些乜乜狀元原全不代表一定是天才。而嚴格來說也不能單憑IQ分數 ...

Don't forget HK's mean is close to 110.
Sure, few geniuses achieve more than ordinary people.

laorenjia

點解睇唔到shadeslayer個post? Can we have it reposted?

laorenjia

bladerunner 發表於 15-3-30 17:22
香港的平均IQ是否真的 close to 110? 有正式大型及可信的統計數據嗎？在沒有可信的資料前，我不會輕易運用 ...

Decided not to wait for shadeslayer's repost which could possibly be similar to what I'm going to say. HK has been consistently ranked as one of the most brainy areas in the world by various surveys. Just google it.

Being a genius is a curse instead of a blessing.

I talked to a few people a few years ago who are teaching maths in university and high school. We came to a consensus that what 沈 had achieved was not too difficult when you came to consider that an adult was giving up his whole life spoon feeding a kid in just one area. Let's see what 沈 is going to achieve when he finishes his PhD. To me, what was done by the son of one of our old friends here was much more difficult and for that I call him a genius or a near genius.