Truth-tellers and liars
On an island, every person is either a truth-teller, who only says true things, or a liar, who only says false things. Jack says, "Ivy and I are of different kinds." Ivy says, "Noor is a liar." Noor says, "Jack is a liar."
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. Start with the statement that gives someone away whoever 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. Start with the statement that gives someone away whoever 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.