Can you solve it? Are you smarter than a Navy admiral? | Mathematics

Tanya Khovanova is a leading authority on the recreational mathematics scene. She is a top blogger and also runs Number Gossip, a site where you can submit a number and she will “tell you everything you wanted to know about it but weren’t afraid to ask.”

Tanya has now written her first book, Mathematical puzzles and curiosities, in collaboration with two other puzzle enthusiasts, Ivo David and Yogev Shpilman. It’s full of fantastic new puzzles and twists on old ones.

Here are three that I liked.

1. Battleships

You are a Navy admiral, charged with an important mission. You have two choices.

a) Send a single ship whose chance of success is P percent.

b) Send two ships, each of which has a chance of success of P/2 percent. At least one ship must succeed for the mission to be a success.

What is your best option?

2. The two oracles

Before you are two oracles, Randie and Rando, who will answer yes or no to all your questions.

Randie randomly answers yes or no to all questions.

Rando randomly decides whether to tell the truth or lie for each question, then answers the question accordingly.

Is there a way to differentiate them? If so, what is it?

3. Bad calculations

Johnny’s homework is to calculate 5548-5489. The answer is 59. He thought the 548 canceled out, leaving 59.