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Three ladies A, B and C have a discussion, where each lady says the truth twice and lies once.

  1. A: B is two years older than me
  2. B: C is 38 years old
  3. C: A is older than me
  4. B: The age difference between C and me is three years
  5. C: A is 36 years old
  6. A: I'm 35 years old
  7. B: At least one of A or C is younger then me
  8. A: I'm one year older than C
  9. C: A is three years younger than B

What is the age of each of the three ladies?

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1 Answer 1

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A says:

  • $B = A + 2$
  • $A = 35$
  • $A = C + 1$

B says:

  • $C = 38$
  • $|B - C| = 3$
  • $A < B$ or $C < B$

C says:

  • $A > C$
  • $A = 36$
  • $B = A + 3$

Notice that

A and C have two pairs of conficting statements. This means that they are both correct on one and wrong on the other. And their remaining statements are both true.
Thus $A = C + 1$ and $A > C$ are true. Also, $A = 35$ or $36$.

This means that

$C = 34$ or $35$, making the statement $C = 38$ false.
Therefore the other two statements of B are true.

Now we see that

$|B - C| = 3$ means that $B, C$ have different parity.
But we also know $A = C + 1$, hence $A, B$ have the same parity.

This forces

$B = A + 3$ to be false, thus $A = 36$, $C = 35$ and $B = A + 2 = 38$.

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  • $\begingroup$ just beat me to it! well done $\endgroup$
    – juicifer
    Dec 6, 2021 at 19:56
  • $\begingroup$ One problem with your logic - "both correct on one and wrong on the other" is not true. The two conflicting statements could have both been lies. $\endgroup$
    – Rob Watts
    Dec 6, 2021 at 20:01
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    $\begingroup$ @RobWatts In each pair of conflicting statements, at least one is false. There are two pairs of conflicting statements between A and C, thus at least two of these statements are false. But A and C have only two false statements in total, one for each. Therefore there is no other false statement - in particular, in each conflicting pair, exactly one statement is false. $\endgroup$
    – WhatsUp
    Dec 6, 2021 at 20:19
  • $\begingroup$ I see what I missed. "A and C have two conficting statements" would be better as "A and C have two pairs of conflicting statements." $\endgroup$
    – Rob Watts
    Dec 6, 2021 at 20:48
  • $\begingroup$ @RobWatts Ah, I see. Thanks for pointing out. I updated the answer to make this clear. $\endgroup$
    – WhatsUp
    Dec 6, 2021 at 20:55

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