While taking a study break, we noticed flyers lying around with the following puzzle:

Hans is creating a display of exactly six items—a razor, a stereo, a television, a UV lamp, a video camera, and a watch—for the Traveler’s Emporium. He arranges the items first through sixth, from left to right, along a shelf. Each item in the display is either powered by an adaptor or by batteries, but not by both. The following conditions apply:

  • The UV lamp is either the leftmost or the rightmost item on the shelf.
  • No item powered by batteries is adjacent to any other item powered by batteries.
  • The watch is powered by batteries.
  • The fourth item on the shelf is not powered by an adaptor.
  • The razor, which is powered by batteries, is to the left of the watch, and to the right of the video camera and the stereo.

1. Which of the following could be true?
(a) The UV lamp is the sixth item on the shelf.
(b) The razor is the third item on the shelf.
(c) The fifth item on the shelf is powered by batteries.
(d) The stereo is powered by batteries.
(e) Both the UV lamp and the video camera are powered by batteries.

2. Which of the following must be true?
(a) The television is the fifth item on the shelf and it is powered by an adapter.
(b) The stereo is the third item on the shelf and it is powered by an adapter.
(c) The video camera is the third item on the shelf and it is powered by batteries.
(d) The video camera is the second item on the shelf and it is powered by an adapter.
(e) The UV lamp is the sixth item on the shelf and it is powered by batteries.

3. If the UV lamp is powered by batteries, each of the following must be true EXCEPT:
(a) The stereo is powered by an adapter.
(b) The video camera is powered by an adaptor.
(c) The first item on the shelf is powered by batteries.
(d) The second item on the shelf is powered by an adapter.
(e) The stereo is the third item on the shelf.

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