Puzzle two brother and facebook by tree

1. Puzzle | Two Brothers and
Facebook by tree
Hup university
6-2-2018

2. Puzzle
• Sahil and Ritik are brothers. One day they were discussing who is
smarter. But gradually the discussion turned into an argument.
Mother came and tried to handle the situation. She gave them a
problem to solve and the one who will solve the problem first,
would be considered smarter than the other. The problem is
• :
In a group of 6 people, you might find some people are friends on
Facebook, or you might find that no one is friend on Facebook. The
brothers are supposed to prove that there is always a group of 3
people where either :
•
–All3 people are mutual friends on Facebook.
• –All3 people are strangers (i.e, no one is friend on Facebook).
• Can you help the brothers to reach to the solution ?

3. Puzzle
• FACT:- 6 people {A,B,C,D,E,F}
• Rules:- X, Y, Z, N, M, P  {A,B,C,D,E,F}
• (friend(XYZ), not-friend(MNP))
• X YZ ≠ NMP.
• If (ch  friend ) then ch  not-friend
ch  {A,B,C,D,E,F}
• If (ch  not-friend ) then ch  friend
ch  {A,B,C,D,E,F}

4. A with {B, C, D,E, F}
A
(AB,CDEF)
(AC,BDEF)
(AD,BCEF)
(AE,BCDF)
(AF,BCDE)
1 2 3 4

5. AB with {C, D, E, F}
(AB,CDEF)
(ABC,DEF)
(ABD,CEF) (ABE,CDF)
(ABF,CDE)
1

6. ( Friends, not Friends)
1 (ABC,DEF)
2 (ABD,CEF)
3 (ABE,CDF)
4 (ABF,CDE)

7. AC with { D, E, F}
(AC,BDEF)
(ACD,BEF) (ACE,BDF)
(ACF,BDE)
2

8. (friend, not friend)
1 (ABC,DEF)
2 (ABD,CEF)
3 (ABE,CDF)
4 (ABF,CDE)
5 (ACD,BEF)
6 (ACE,BDF)
7 (ACF,BDE)

9. AD with {E, F}
(AD,BCEF)
(ADE,BCF)
(ADF,CEF)
3

10. (friend, not friend)
1 (ABC,DEF)
2 (ABD,CEF)
3 (ABE,CDF)
4 (ABF,CDE)
5 (ACD,BEF)
6 (ACE,BDF)
7 (ACF,BDE)
8 (ADE,BCF)
9 (ADF,CEF)

11. AE with {F}
(AE,BCDF)
(AEF,BCD)
4

12. (friend, not friend)
1 (ABC,DEF)
2 (ABD,CEF)
3 (ABE,CDF)
4 (ABF,CDE)
5 (ACD,BEF)
6 (ACE,BDF)
7 (ACF,BDE)
8 (ADE,BCF)
9 (ADF,CEF)
10 (AEF,BCD)

13. B with {C, D,E, F}
B
(BC,ADEF)
(BD,ACEF)
(BE,ACDF)
(BF,ACDE)
1 2 3

14. BC with {D, E, F}
(BC,ADEF)
(BCD,AEF) (BCE,ADF)
(BCF,ADE)
1

15. (friend, not friend)
1 (ABC,DEF), (ABD,CEF), (ABE,CDF), (ABF,CDE)
5 (ACD,BEF), (ACE,BDF), (ACF,BDE)
8 (ADE,BCF), (ADF,CEF)
10 (AEF,BCD)
11 (BCD,AEF), (BCE,ADF), (BCF,ADE)
13

16. BD with {E, F}
(BD,ACDF)
(BDE,ACF)
(BDE,ACE)
2

17. (friend, not friend)
1 (ABC,DEF), (ABD,CEF), (ABE,CDF), (ABF,CDE)
5 (ACD,BEF), (ACE,BDF), (ACF,BDE)
8 (ADE,BCF), (ADF,CEF)
10 (AEF,BCD)
11 (BCD,AEF), (BCE,ADF), (BCF,ADE)
14 (BDE,ACF), (BDE,ACE)
16

18. BE with {F}
(BE,ACDF)
(BEF,ACD)
3

19. (friend, not friend)
1 (ABC,DEF), (ABD,CEF), (ABE,CDF), (ABF,CDE)
5 (ACD,BEF), (ACE,BDF), (ACF,BDE)
8 (ADE,BCF), (ADF,CEF)
10 (AEF,BCD)
11 (BCD,AEF), (BCE,ADF), (BCF,ADE)
14 (BDE,ACF), (BDE,ACE)
16 (BEF,ACD)

20. C with {D,E, F}
C
(CD,ABEF)
(CE,ABDF)
(CF,ABDE)
1 2

21. CD with {E,F}
(CD,ABEF)
(CDF,ABE)
1
(CDE,ABF)

22. (friend, not friend)
1 (ABC,DEF), (ABD,CEF), (ABE,CDF), (ABF,CDE)
5 (ACD,BEF), (ACE,BDF), (ACF,BDE)
8 (ADE,BCF), (ADF,CEF)
10 (AEF,BCD)
11 (BCD,AEF), (BCE,ADF), (BCF,ADE)
14 (BDE,ACF), (BDE,ACE)
16 (BEF,ACD)
17 (CDE,ABF), (CDF,ABE)

23. CE with {F}
(CE,ABDF)
(CEF,ABD)
2

24. (friend, not friend)
1 (ABC,DEF), (ABD,CEF), (ABE,CDF), (ABF,CDE)
5 (ACD,BEF), (ACE,BDF), (ACF,BDE)
8 (ADE,BCF), (ADF,CEF)
10 (AEF,BCD)
11 (BCD,AEF), (BCE,ADF), (BCF,ADE)
14 (BDE,ACF), (BDF,ACE)
16 (BEF,ACD)
17 (CDE,ABF), (CDF,ABE)
19 (CEF,ABD)

25. D with {E, F}
D
(DE,ABCF)
(DF,ABCE)