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# Date of the Dinner

## Question

That 'Math Council Dinner' is in December, but I forgot which night, so I asked around. Alan said that the date was an odd number; Brenda claimed it was greater than 13. Carly declared it was not a perfect square, while Dara swore it was a perfect cube. Finally, Edward told me the date was less than one-fourth his age, which I know to be 68. Yesterday I learned that only one of them had told the truth! What is the date of the dinner?

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If Brenda was wrong, then the date was not greater than 13.

If Edward was wrong, then date was greater than 17.
So one of them must be correct & other must be wrong.
Let us assume Brenda was right, and every one else was wrong. Then:
Brenda was right, so date was greater than 13.
Alan was wrong, so date was not an odd number; So possible dates are 14,16,18,20,22,24,26,28,30.
Carly was wrong so the date was a perfect square; only date 16 is the perfact square in the above list of possible dates.
Dara was wrong, so date was not a perfect cube. The date 16 is not a perfect cube.
Edward was wrong, so the date was greater than 17. But 16 is less than 17, so 16 is not the date.
Conclusion of above is that Brenda is not right; Therefore Edward must be right & every one else was wrong. Then:
Edward was right, so the date was less than 17.
Alan was wrong, so the date was not an odd nuber. So the possible dates are 16,14,12,10,8,6,4,2.
Brenda was wrong so the date was not greater than 13; so remaining possible dates are 12,10,8,6,4,2.
Carly was wrong so the date was a perfect square; only 4 is the date which is a perfect square.
Dara was wrong so the date was not a perfect cube; the date 4 is not a perfect cube.

Answer: The dinner date is 4th December.

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well explained!

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