# Lying to the young

## Puzzle

Alex, Brook, Cody, Dusty, and Erin recently found out that all of their birthdays were on the same day, though they are different ages.

On their mutual birthday, they were jabbering away, flapping their gums about their recent discovery. And, lucky me, I was there. Some of the things that I overheard were...

• Dusty said to Brook: "I'm nine years older than Erin."
• Erin said to Brook: "I'm seven years older than Alex."
• Alex said to Brook: "Your age is exactly 70% greater than mine."
• Brook said to Cody: "Erin is younger than you."
• Cody said to Dusty: "The difference between our ages is six years."
• Cody said to Alex: "I'm ten years older than you."
• Cody said to Alex: "Brook is younger than Dusty."
• Brook said to Cody: "The difference between your age and Dusty's is the same as the difference between Dusty's and Erin's."

Since I knew these people -- and how old they were, I knew that they were not telling the whole truth.

After thinking about it, I realized that when one of them spoke to someone older, everything they said was true, but when speaking to someone younger, everything they said was false.

How old is each person?

## References

Maths is Fun - math and logic puzzles appropriate for math education.