Truth Teller & Liar Question

John, Paul, George and Ringo all enter a race, but there is nobody at the finish line to judge the ending. When the judge finally shows up to award the prize for coming in first, these are the statements the four of them make:

John: I was neither first nor last. Paul: I did not finish last. George: I won the race! Ringo: I came in last.

The judge does not know what to do when Yoko, who was watching the race, says, “Exactly one of these four is lying.”

To whom should the judge grant the prize?

#Logic

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

If John was the liar, then George and Ringo must be telling the truth, but they're statements contradict as John was either first or last, but so were George and Ringo. So John is telling the truth.

If Paul was the liar, then he finished last. But as Ringo is telling the truth, Ringo must be last. So Paul is also a truth teller.

If Ringo is lying, then he/she is either 1st, 2nd or 3rd. Then, as the others are telling the truth, John wasn't last, Paul wasn't last and George wasn't last as he was first. Someone has to be last, so Ringo must not be lying.

This leaves George, that sneaky liar, I'll tell his mom to ground him.

But the question asks for the winner. Since John couldn't be first or last, Ringo was last, and George wasn't first because he is lying, Paul must be first.

@Half pass3

A Former Brilliant Member - 8 months, 3 weeks ago

paul

george would only win if all were telling truth

if paul lys then what about ringo

of ringo lies then there is two people either sharing second or third

NSCS 747 - 8 months, 2 weeks ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$