See https://learn1.open.ac.uk/mod/oublog/viewpost.php?post=244360
Given all three labels are wrong, there are only two possible combinations.
1) Label A & P - contents A Label A - contents P Label P - contents A & P
2) Label A & P - contents P Label A - contents A & P Label P - contents A
If we take a fruit from A & P as we are permitted inspecting it will tell which of 1) and 2) is correct.
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HI RICHARD,
I CAN SEE THE LOGIC OF YOUR IMPRESSIVE PRESENTATION. I WAS WONDERING IF YOU WOULD AGREE WITH ME THAT BY TAKING A FRUIT FROM THE A & P BAG I WOULD IMMEDIATELY IDENTIFY THE CONTENTS OF THAT BAG AND I CAN THEN ATTACH THE CORRECT LABEL FROM ONE OF THE OTHER BAGS . THAT BEING SO, IF I STICK THE LABEL A & P TO MY HAND I'M LEFT WITH ONE WRONGLY LABELLED BAG AND ONE UNLABELLED BAG. I KNOW THE LABELLED BAG IS INCORRECTLY LABELLED SO THERE IS ONLY ONE BAG TO WHICH ITS LABEL CAN BE ATTACHED CORRECTLY, NAMELY THE UNLABELLED BAG. I THEN TAKE THE A&P LABEL FROM MY HAND AND ATTACH IT TO THE LAST OF THE THREE BAGS. ALL SHOULD NOW BE CORRECTLY LABELLED.
I THINK THE SOLUTION TO THE PROBLEM LIES IN OPENING THE A & P BAG BECAUSE I CAN THEN IMMEDIATELY IDENTIFY ITS CONTENTS. OPENING ANY OTHER BAG FIRST LEAVES TWO POSSIBLE CHOICES OF CONTENT.
VERY INTERESTING POSTING,
JOSEPH.