At the end of the graduation and commissioning ceremony at the United States Naval Academy in Annapolis, newly minted officers (now ensigns) participate in the “cover toss”; they throw their white dress hats into the air. It’s a long-standing Naval Academy tradition symbolizing the transition from midshipman to officer.

They’ve graduated. They don’t need their old hats anymore. They all get new hats representing their new rank.

It’s hard to keep a lid on these kids.

So here’s this week’s Microsofty: Assume there are 1,000 graduates and their hats are scattered everywhere. Every graduate picks up a hat to keep as a souvenir or give to parents. Hopefully they all pick up their own. But what is the probability that exactly 999 of the graduates end up with their original hat?

Solution to Microsofty 96:  The Queens Problem

Here’s last week’s puzzle: On  an 8×8 chessboard, 8 queens are placed so that no queen can capture another. This is the classic Queens problem.

One solution is shown in the figure. The board can be rotated but there will still be a solution to the Queens problem. So there are other possible answers as well.  

The Monday Microsofty is a weekly feature of Mind Matters News. Here are the links to all the puzzles and answers to date:

Monday Microsofty 96:  The Queens Problem: Can you place 8 queens on a standard 8×8 chessboard so that no queen can capture another? To solve last week’s dilemma, pay attention to the different functions words can have in a sentence.

Monday Microsofty 95: I told you her name but …You weren’t listening. Getting to the core of a problem doesn’t need to involve math. Here’s one that doesn’t. To answer last Monday’s tree planting dilemma, look for shapes other than squares.

Monday Microsofty 94:  A Tree Planting Dilemma This week’s puzzle sounds simple but it involves thinking in terms other than squares. The answer to last week’s “count the squares” puzzle can be turned into a formula that can be applied to any number of dimensions.

Image Credit: Cobalt - Adobe Stock

Monday Microsofty 93: Square dance with the mathematicians! How do we determine how many squares there are in squares of squares? Or cubes of cubes? Hint for the handshake problem in Microsofty 92: Friedrich Gauss (1777–1855) provided a formula for this.

Monday Microsofty 92: When the nerd enters a room… Shaking hands is expected. Here’s a math question about the custom, to delight the true nerds among us. A hint for Microsofty 91: Where might Jimmy the Mooch have found some spare energy? You can find links and answers to Microsofties 91 through 87 here as well.

Monday Microsofty 87: Are you as good a detective as you think? Here’s a test from the world of codebreaking To solve last week’s puzzle, look up the definition of “calorie.” Are we using the word to mean the same thing? You can find links and answers to Microsofties 77 through 86 here as well.

Monday Microsofty 76: The Smoking Gun explains a computer scientist or engineer, a law enforcement officer often relies on abductive reasoning to crack a case, so with this in mind, you will have to crack last week’s puzzle. You can find links and answers to Microsofties 55 through 75 here as well.

Image Credit: thaninee - Adobe Stock

Monday Microsofty 55: “It happens every spring.” Baseball, that is. Here’s a puzzle that takes in baseball’s summer. To solve last week’s puzzle, you don’t need to know the distance. Check the problem again for the number you do need to know. You can find links and answers here to Microsofties 51 through 54 as well.

Monday Microsofty 50: Cutting through the cornbread. How did Yuri Senior cut the cornbread into eight identical portions using only three straight cuts? You can guess the answer to Microsofty 49 if you try the test question yourself at home, using a small mirror. You can find links and answers here to Microsofties 46 through 49 as well.

Monday Microsofty 45: Can Tony beat the fast-food curfew? An early curfew on fast food service motivated a boy to exercise more vigorously. But how fast was he pedalling? To solve Micro Softy 44, recall that Tony doesn’t need to take the individual pills each day, only the prescribed amount of each. You can find links and answers here to Micros Softies 41 through 44 as well.

Monday Microsofty 40: The fate of a false prophet. He wasn’t actually fired for being a false prophet but for something that his prophecy unintentionally revealed. The solution to Micro Softy 39 lies in considering an alternative possible meaning of a word commonly used in sports. You can find links and answers here to Micro Softies 30 through 39 as well.

Monday Microsofty 29: A funeral lament in four lines. The funeral director was puzzled by Dan’s description of his relationship to the deceased but there was no question that his grief was sincere You can find links and answers here to Microsofties 22 through 29 as well.

Monday Microsofty 21: Finding More of the Deadly Fentanyl Pills. You can find links and answers here to Microsofties 11 through 20 as well.

Monday Microsofty 11: What Happened to That Other Dollar? You can find links and answers here to the first ten Micro Softies. Have fun!