Puzzle two brother and facebook by tree
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1. Two brothers, Sahil and Ritik, were arguing about who was smarter and their mother gave them a problem to solve to determine a winner. 2. The problem involved proving that in any group of 6 people, there would always be a subgroup of 3 people who were either all friends on Facebook or all strangers with no connections. 3. The document then proceeds to systematically list out all the possible friendship combinations of subgroups of 3 people from a group of 6 people labeled A through F, ultimately proving that the problem can be solved.
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)
- 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
- 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
- 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)
- 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)