And the winners are...

The winners of the June Mathville puzzle are:

Seth McElroy, winner of a $30 gift card to the PVCC bookstore.

Jackie Meurer, winner of a $15 gift card to the Mermaid coffee cart.

Michael Do, winner of a BIG Hershey's milk chocolate bar.

Congratulations, winners! Please pick up your prizes at the library by June 19th, 2014, at 8 p.m.

Thank you to all who played!

And now the solution:

If you open the box labeled SCARVES or the box labeled GLOVES first, you cannot be sure of what is inside. For example, if you open the box labeled SCARVES and take out a glove, you could have the GLOVES box or the GLOVES & SCARVES box.

To be positive, you should open the box labeled GLOVES & SCARVES first. Because all the boxes are mislabeled, you know that this box does not have the two objects, but has either gloves OR scarves. So whatever object you remove from the box is what the box contains.

So you stick your hand in and remove one object. 

If the object is a glove, then you know the box has only gloves. This leaves you with two mislabeled boxes: one labeled gloves, the other labeled scarves. You know both are mislabeled, so all you have to do is switch the labels. 

If the object is a scarf, then you know the box has only scarves. This leaves you with two mislabeled boxes, so you switch the labels.