Weighing All

What four weights can be used to balance from 1 to 30 pounds?




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I ask Joseph to pick any 5 cards out of a deck with no Jokers.

He can inspect then shuffle the deck before picking any five cards. He picks out 5 cards then hands them to me (Jack can't see any of this). I look at the cards and I pick 1 card out and give it back to Joseph. I then arrange the other four cards in a special way, and give those 4 cards all face down, and in a neat pile, to Jack.

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In the addition below, all digits have been replaced by letters. Equal letters represent equal digits and different letters represent different digits.
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BBDCAA
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ABDBAA
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Before reading ahead, you must know the fact that only one of the people here is telling the truth.

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