Truth-tellers and liars, step by step
On an island each person only ever tells the truth or only ever lies.
How many of the three are liars?
Anchor one islander, then follow the chain
- Three islanders, each a truth-teller who only says true things or a liar who only says false ones. Three statements, and the trick is to start with the one that gives someone away no matter who said it.
- Jack says Ivy and Jack are of DIFFERENT kinds. Whether Jack is honest or lying, that claim makes Ivy a liar — a truthful "different" is true, and a lying "different" means they are really the same as a liar.
- Now Ivy is known, so Ivy's statement about Noor is settled: a liar saying it makes Noor a truth-teller. And then Noor's statement about Jack makes Jack a liar.
- So Ivy is a liar, Jack is a liar and Noor is a truth-teller — 2 of the three are liars.
How it works.
- 01
Three islanders, each a truth-teller who only says true things or a liar who only says false ones. Three statements, and the trick is to start with the one that gives someone away no matter who said it.
- 02
Jack says Ivy and Jack are of DIFFERENT kinds. Whether Jack is honest or lying, that claim makes Ivy a liar — a truthful "different" is true, and a lying "different" means they are really the same as a liar.
- 03
Now Ivy is known, so Ivy's statement about Noor is settled: a liar saying it makes Noor a truth-teller. And then Noor's statement about Jack makes Jack a liar.
- 04
So Ivy is a liar, Jack is a liar and Noor is a truth-teller — 2 of the three are liars.