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The Age-Old Lie


A reporter on New Year's Eve 1993 wanted to know, from Pat and Chris, how old they were, but felt (correctly, it turns out) that one would lie. So the reporter asked them both, "Write down your age now, your age at the end of next year, add these together, then multiply the result by 5," quickly followed by: "now add the last digit of the year you were born." They had no time to fake that last digit; Pat answered 281, while Chris announced 229. Who was lying, and what were their real ages at the time?

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Pat is 27 and told the truth. See analysis below.

Chris then lied.

Let's assume he ONLY lied about his present age and was accurate otherwise.

Without that restriction we can't conclude very much.

Chris used an age of xy.

He then calculated an age plus age next year times 5 to be xy5.

Adding last digit of birth year gave 229,

so he claimed to be 22 in 1993 with a birth year ending in 4.

That is impossible.

Chris' age actually is 9, 19, 29, 39, ...

If he's about the same age as his friend Pat, he's 29.

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