Classic black and white film who I believe Peter Falk starred in. Set at a summer camp and they discover a book is missing. Throughout whole movie they are trying to find out who stole this book. Where book went missing there was carrot remains. So one guy goes around asking people "By the way do you like carrots?" He tries to serve people carrots to try and find the person who took this book. I need the title of this movie. Please help!