Known for spying on millions of Americans The National Security Agency (NSA) has a bad reputation. However, in order to break intelligent codes some of the smartest people have to work there, without a doubt. These individuals must be really good at solving puzzles and riddles, it’s part of their job.
That’s why The NSA makes them create their own puzzles and teasers.
Every month, the NSA publishes on its website a brain-teaser written by an employee that members of the public can try their hand at. One month it’s a maths challenge created by an applied research mathematician; the next it’s a logic puzzle by a systems engineer. They’re all published in what the NSA calls its “Puzzle Periodical.”
NSA applied mathematician submitted a brilliant and surprisingly easy brain teaser to check if someone is smart enough to get into The NSA!
Here it is:
“On a rainy summer day, brothers Dylan and Austin spend the day playing games and competing for prizes as their grandfather watches nearby. After winning two chess matches, three straight hands of poker and five rounds of ping-pong, Austin decides to challenge his brother, Dylan, to a final winner-take-all competition. Dylan clears the kitchen table and Austin grabs an old coffee can of quarters that their dad keeps on the counter.
The game seems simple as explained by Austin. The brothers take turns placing a quarter flatly on the top of the square kitchen table. Whoever is the first one to not find a space on his turn loses. The loser has to give his brother tonight’s dessert. Right before the game begins, Austin arrogantly asks Dylan, “Do you want to go first or second?”
Dylan turns to his grandfather for advice. The grandfather knows that Dylan is tired of losing every game to his brother. So he tells him what to do. Dylan wins! What does the grandfather whisper to Dylan?”
This is one of those puzzles that when you see the solution you’ll think ‘how did I not think of this?!’
It’s all in the geometry and the mathematics. That’s all I am going to say.
Try to solve it. When you REALLY know that you cannot solve it or if you think of some solution, scroll down for the answer. This is truly a brilliant puzzle!
Here is the solution:
Dylan should go first. By doing this, Dylan can guarantee a win by playing to a deliberate strategy. On his first turn, he can place a quarter right on the center of the table. Because the table is symmetric, whenever Austin places a quarter on the table, Dylan simply “mirrors” his brother’s placement around the center quarter when it is his turn. For example, if Austin places a quarter near a corner of the table, Dylan can place one on the opposite corner. This strategy ensures that even when Austin finds an open space, so can Dylan. As a result, Dylan gains victory, since Austin will run out of free space first!
Submitted by Sean A., NSA Applied Mathematician;