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UPDATE (2 August): Anything with less than 2 people is not
a party. All party acquaintance graphs must have n>1.
The following riddle comes from Dominic van der Zypen. (Thanks, Dominic!) It has two parts. Answer both for credit. n people are at a party. Every pair of them has exactly k mutual acquaintances among the n. Acquaintance is a symmetric and anti-reflexive relation. Part 1:Describe an infinite family of party acquaintance graphs that satisfy the criteria above, all with k=1.Part 2:Describe at least two distinct party acquaintance graphs that satisfy the criteria above with k=2, or prove such do not exist. |
List of solvers:Jim Boyce (2 August 22:06)Kuan Yang (2 August 22:33) Lorenz Reichel (3 August 07:36) Radu-Alexandru Todor (4 August 08:58) Lin Jin (6 August 07:12) Bart De Vylder (7 August 00:10) JJ Rabeyrin (7 August 17:39) Gaoyuan Chen (16 August 19:10) Joseph DeVincentis (17 August 03:56) Daniel Bitin (26 August 18:36) Oscar Volpatti (31 August 03:45) |
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The solution will be published at the end of the month.
Enjoy!