What's the maximum number of liars among them?
Calculus
Level
3
14 people are seated around a roundtable. Each person either always lies, or always speaks the truth. Everybody says: “The people to my left and to my right are liars”. What is the maximum number of liars among them?
The answer is 9.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
L for Liars and T for Truth Tellers.
[LTL][LTL][LTL][LTL]
Every T needs 2 Ls to sandwich him / her. Maximizing, we get 4 trios of those by floor(14/3) = 4. The last two people would be sandwiched between 2 Liars, so they can't be both of the same tribe.
L _ _ L
==> L L L L ❌
==> L T T L ❌
==> L T L L ✔️
==> L L T L ✔️
Answer
= { 2 knaves } × { 4 trios } + { 1 of the opposite pair }
= 9