[puzzle] Two DIFFICULT Cases, Can You Solve Them? (the ANSWER)

INTRO

Well, I love puzzles and difficult math questions. But these two are very special for me.
They made me :

• realized that there are PROBLEMS only possible to answer by analyzing what other people think or say or do.
• realized that when people say something to you, there are messages (somethime it is hidden) in their words.
• realized that you need to listen to (not hear) people, because what they say might contain some part of answer you’re looking for.

Here’s the answer, and again, for BAHASA, pls see below.

ANSWER TO FIRST QUESTION

Let’s assume that person in the back = C, in the middle = B, in the front= A.

The key to answer this question is to understand that there is ‘something’ in someone’s words.

PART 1 – What C said

The ONLY combination that C would know his hat is if C saw both A and B wear BLUE (because there were only TWO BLUE hats, so C would know he wears RED).

So, C would see one of these combination (ZERO BLUE or ONE BLUE) :
Alternative 1 : A-RED B-RED
Alternative 2 : A-RED B-BLUE
Alternative 3 : A-BLUE B-RED

PART 2 – What B said

B (and you) would know now, the possible combination of A & B caps are :
Alternative 1 : A-RED B-RED
Alternative 2 : A-RED B-BLUE
Alternative 3 : A-BLUE B-RED

Look at the combination!
If B saw A wear BLUE, then B will know his/her hat is RED.

B looked A’s hat, and B still didn’t know what color his/her cap was.

So, you (and A) must realise that the possible combinations are :
1. A-RED B-RED, and
2. A-RED B-BLUE

In both scenario, A will wear RED. So he knew it!!

SECOND QUESTION

Aaaah… this is very difficult, even only to understand it.

Let’s begin with the the fact that all monks can see other monks’ forehead, but not their own forehead.

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Case A. Let’s Assume : There is ONLY ONE monk who has RED-mark (X=1)

Day 1

• There are 49 monks that will see ONE person has RED mark in the forehead (monks with BLUE mark)
• There is 1 monk that will see there is nobody has RED mark (this is the monk with RED mark)
• So at Day 1-Midnight, this 1 monk (who see no one with RED mark) will leave the hall.
• Case closed.

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Case B. Let’s Assume : There are TWO monks who has RED-mark (X=2)

Day 1

• There are 48 monks (with Blue mark) that will see TWO persons have RED mark in the forehead.
• There are 2 monks (with Red mark) that will see ONE person has RED mark.
• But these 2 monks cannot conclude they must leave the hall, since there might be possibility of “Only 1 monk has RED mark” (like we analyse in Case A)
• So at Day 1-Midnight, NOBODY will leave the hall.

Day 2

• NOBODY left yesterday. All monks now understand that there must be more than 1 RED mark.
• And all the monks know that this means : whoever see 1 (X minus 1) mark, must leave tonight.
• So at Day 2-Midnight, TWO monks (those who see 1 RED Mark) will leave the hall.
• Case closed.

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Case C. Let’s Assume : There are THREE monks who has RED-mark (X=3)

Day 1

• There are 47 monks that will see THREE persons have RED mark in the forehead.
• There are 3 monks that will see TWO person has RED marks.
• So at Day 1-Midnight, NOBODY will leave the hall.

Day 2

• NOBODY left. All monks now understand that there must be more than 1 RED mark.
• And all the monks know that this means : whoever see 1 mark, must leave tonight.
• However, nobody sees only 1 mark.
• So at Day 2-Midnight, nobody leaves the hall.

Day 3

• NOBODY LEFT AGAIN! All monks now understand that there must be more than 2 RED mark.
• And all the monks know that this means : whoever see 2 (X minus 1) mark, must leave tonight.
• So at Day 2-Midnight, THREE monks (that see 2 RED Mark) will leave the hall.
• Case closed.

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So we can continue this, we can conclude :

• Then, at day number X, at midnight, all of RED-marked-forehead monk(s) will leave the hall at the same time.
• This/these monk(s) is/are monk(s) that would see there is/are (X minus 1) RED mark(s) in the 49 monk’s forehead.

Amazing huh? But can you imagine if there’s one monk who doesn’t understand the whole concept? It will ruin everthing, cause no one will ever leave the building

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JAWABAN PERTANYAAN 1

Kita sebut orang di belakang= C, di tengah = B, di depan = A.

Kunci menjawab ini adalah menyadari bahwa ada sesuatu di omongan/jawaban seseorang.

PART 1 – Jawaban si C

Si C pasti tahu dia pakai topi warna apa kalau dia liat kedua teman di depan pakai BIRU.
Kenapa? Karena cuma ada DUA topi BIRU. Jadi kalau dia liat, pasti tahu dia pakai warna MERAH.

Jadi pastilah si C itu lihat SATU BIRU atau DUA BIRU. Ada tiga alternatif :

Alternative 1 : A pakai MERAH, B pakai MERAH
Alternative 2 : A pakai MERAH, B pakai BIRU
Alternative 3 : A pakai BIRU, B pakai MERAH

PART 2 – Jawaban si B

B (dan Anda) tahu dong kombinasi di atas, dari jawaban si C.

Lihat kembali kombinasinya, kalau B melihat si A pakai BIRU, dia tahu topinya MERAH.
Karena di tiga alternatif itu hanya satu skenario yang A pakai BIRU.

Namun B tidak tahu kan? Jadi Anda (dan si A) pasti tahu kombinasi yang tertinggal adalah 1. A pakai MERAh, B pakai MERAH
2. A pakai MERAH, B pakai BIRU

Di kedua alternatif, topi A warnanya … MERAH! Makanya dia tahu.

PERTANYAAN KEDUA

Tarik nafas.. ini susah.

Fakta penting : semua calon biksu TIDAK BISA lihat dahinya sendiri tapi BISA melihat dahi orang lain!!!

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Skenario A. Mari berandai, cuma SATU calon biksu yang dapat merah di dahinya (X=1)

Day 1

• Berarti ada 49 calon biksu yang melihat 1 orang berdahi MERAH.
• Berarti ada 1 calon biksu yang melihat semua orang berdahi biru.
• Maka, di malam hari, si 1 calon biksu itu pergi, karena dia tahu tidak semua lolos.
• Case closed.

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Skenario B. Mari berandai, ada DUA calon biksu yang dapat merah di dahinya (X=2)

Day 1

• Ada 48 calon biksu yang melihat 2 orang berdahi MERAH
• Ada 2 calon biksu yang melihat 1 orang berdahi MERAH
• Namun 2 calon biksu ini tidak pergi malam itu, karena merasa bisa saja cuma 1 calon biksu yang dapat MERAH

Day 2

• TIDAK ADA yang pergi semalam.
• Semua calon biksu jadi tahu, ada lebih dari 1 yang berdahi MERAH.
• Dan semua jadi tahu, siapa pun yang lihat 1 orang berdahi MERAH harus pergi.
• Di malamnya, 2 calon biksu pergi.

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Ngerti kan?