You're handed a deck of cards with N of the cards face-up ... You can't see the cards. How would you split the cards into two piles, with the same number of face-up cards in each pile?Solution is at the end of this post.
The suggested cataloging is HF5549.5 - Personnel Management. This is the second book: a tutorial on the types of questions popular in Silicon Valley and other places looking for highly creative and/or intelligent employees. Though the Google connection offers some updated information, most of the advice and puzzles are decades or even centuries old. Since the interviewing advice ends before the middle of the book ... the remainder is puzzles solutions ... I would have cataloged under QA95 - Mathematical Recreations. Though if you are new to the job market for scientists and mathematicians with advanced degrees, it is a good review.
Before the solution of the puzzle, I have a personal note. Arthur C Clarke said,
Any sufficiently advanced technology is indistinguishable from magic.Practically this means that the more you know, the less magic there is in the world - sometimes a sad result. In grad school, I had the privilege of taking a problem solving course from Ivan Sutherland. One question that impressed me was the puzzle of why all jumping animals (crickets, rabbits, kangaroos, people, ...) pretty much jump the same height. I've remember this problem for for over 40 years and have always associated it with Ivan. In this book I learned this observation originated in the 17th century by a contemporary of Galileo. My world now has a little less magic.
But here is some magic for your world. Count N cards from the deck and turn that stack over. The proof is left to the reader.