Here is a classic puzzle. I don't know its origin for sure, but I think Martin Gardiner might have published it in his long-standing Scientific American column.
I have three bags and I know one contains apples, one contains pears, and the third both apples and pears.
Each bag is labelled to say what its contents are but unfortunately the labels have got swapped round so all three are wrong.
I am allowed to choose one bag and take out a single fruit. I want to work out what the correct labelling of all the bags should be. How can I do it?
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Lets see:-
the bag with the apples in is marked "apples and pears" or "pears"
the bag with pears is marked "apples" or "apples and pears"
the bag with both apples and pears is marked "apples" or "pears"
am I on the right lines?
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IF I TAKE OUT AN APPLE FROM THE BAG MARKED ‘APPLES AND PEARS’ I KNOW THAT IT IS NOT FROM THE BAG WHICH SHOULD BE MARKED ‘APPLES AND PEARS' BUT FROM THE BAG WHICH SHOULD BE MARKED APPLES. I THEN TAKE THAT LABEL ‘APPLES’ AND ATTACH IT TO THE BAG FROM WHICH I TOOK THE APPLE. I THEN PUT THE LABEL ‘APPLES AND PEARS’ ON THE BAG WHICH IS MARKED ‘PEARS’ BECAUSE IT IS WRONGLY MARKED. I THEN PUT THE ‘PEARS’ LABEL ON THE BAG MARKED ‘APPLES’.
I THINK MY FIRST POSTING IS IN CLOSE AGREEMENT WITH THIS BUT THERE IS A SLIGHT SYNTACTICAL ABBERATION IN THE FIRST.
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STILL NOT HAPPY WITH THE WORDING.
I TAKE AN APPLE FROM THE BAG MARKED 'APPLES AND PEARS' AND BECAUSE I KNOW IT IS WRONGLY MARKED I REMOVE THE LABEL AND TAKE THE 'APPLES' LABEL FROM THE BAG SO MARKED AND APPLY IT TO THE BAG FROM WHICH I TOOK THE APPLE. I NOW HAVE ONE WRONGLY MARKED BAG AND ONE UNLABELLED BAG. I TAKE THE LABEL FROM THE 2ND WRONGLY LABELLED BAG AND APPLY THE LABEL TO THE UNLABELLED BAG. I THEN TAKE THAT LAST LABEL AND APPLY IT TO THE NOW UNLABELLED BAG. ALL SHOULD NOW BE CORRECTLY LABELLED.
I WAS WATCHING A PARTICULARLY INTERESTING DVD AND MY ATTENTION WAS TORN BETWEEN THE POSTING AND THE DVD.