Interview Questions Reloaded

[nguyenxuanson]

hey, I think card game has 52 card=> two set has 104. Any explanation?

[shinichi9htv]

Mọi người nghĩ xong câu con bài chưa để em đưa lời giải

[Khoa Tran]

Originally Posted by shinichi9htv

Mọi người nghĩ xong câu con bài chưa để em đưa lời giải

Unless somebody else wants to solve it, Quân đưa lời giải luôn đi. I guess it involves a lot of IF statements, như cái bài 90 đồng xu gì đó (that problem is nasty ).

[shinichi9htv]

I find this is an interesting problem. Unfortunately, no one wants to solve it

co 5 so a1 < a2 < a3 < a4 < a5

Ta co the chia 1-120 thanh 5 khoang (bo 4 so nhan duoc ra, da'nh so la.i)
1-24, 25-48,.., 107-120

minh xem duoc 4 so a_i1,...,a_i4. Cach sap xep 4 so nay cho ta 1 gia tri k nao do (1<= k <=24). So a_i5 duoc chon se la 1 trong 5 so
k, 24 + k,...,106+k. 5 so na`y chia cho 5 co so du* kha'c nhau.

5 truong hop:
Neu mi`nh giu lai a1 va bo a2,..,a5 thi a_i5 = a1
Neu mi`nh giu lai a2 va bo a1,a3,a4,a5 thi a_i5 = a2-1
... giu lai a3 thi a_i5 = a3-2
... giu lai a4 thi a_i5 = a4-3
... giu lai a5 thi a_i5 = a5-4

Nhu vay ton tai 1 ca'ch bo di ma a_i1 + ... + a_i5 = 0 (mod 5)

Tu do xac dinh duoc a_i5.

[YADD]

Thanks, shinichi, for the answer. I must ponder thru it. Just a few naive comments...

First, why are there 124 cards?

Second, cards are pairwise indistiguishable. How can you number them from 1 to 120?

[Khoa Tran]

Originally Posted by shinichi9htv

Cach sap xep 4 so nay cho ta 1 gia tri k nao do (1<= k <=24).

Chưa hiểu đoạn này lắm. How do you determine k? Mình sắp xếp các con bài geometrically theo kiểu que diêm để signal người thứ 2 à?

[shinichi9htv]

+ ah thuc ra la co' 124 con ba`i, ko lien quan den 2 bo ba`i a.
+ xep 4 con theo thu tu thi co 24 ca'ch xep

[Khoa Tran]

Originally Posted by shinichi9htv

I find this is an interesting problem. Unfortunately, no one wants to solve it

co 5 so a1 < a2 < a3 < a4 < a5

Ta co the chia 1-120 thanh 5 khoang (bo 4 so nhan duoc ra, da'nh so la.i)
1-24, 25-48,.., 107-120

minh xem duoc 4 so a_i1,...,a_i4. Cach sap xep 4 so nay cho ta 1 gia tri k nao do (1<= k <=24). So a_i5 duoc chon se la 1 trong 5 so
k, 24 + k,...,106+k. 5 so na`y chia cho 5 co so du* kha'c nhau.

5 truong hop:
Neu mi`nh giu lai a1 va bo a2,..,a5 thi a_i5 = a1
Neu mi`nh giu lai a2 va bo a1,a3,a4,a5 thi a_i5 = a2-1
... giu lai a3 thi a_i5 = a3-2
... giu lai a4 thi a_i5 = a4-3
... giu lai a5 thi a_i5 = a5-4

Nhu vay ton tai 1 ca'ch bo di ma a_i1 + ... + a_i5 = 0 (mod 5)

Tu do xac dinh duoc a_i5.

Though I'm no longer interested in tricky puzzles, I have to admit that the solution is truly brilliant. Given the solution, it's still not easy to comprehend.

Keep it up

[Khoa Tran]

Here's a fun Physics question to ask during an interview.

Everyone knows that a light ray is reflected in the direction symmetric to the incident ray, with respect to the normal (like in the figure below).



However, the incident ray hits the surface at only one point, say O. Suppose that we rotate the plane around O an angle . The incident ray is the same and the hit point O is the same. But the reflected ray changes. Why is that?

[You may ask the same question with the motion of a super-tiny ball.]

[shinichi9htv]

Originally Posted by nguyenxuanson

given a Brownian motion start from 0 we define the time change

give one presentation of the variable .

It looks like Bougerol's indetity