Tanya Khovanova is a luminary of the recreational mathematics scene. She is one of its foremost bloggers and also runs Number Gossip, a site where you can submit a number and she “will tell you everything you want to know about it but were 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 packed with fantastic new puzzles and twists on old ones.
Here are three I enjoyed.
1. Battleships
You are an admiral in the Navy, in charge of an important mission. You have two choices.
a) To send a single ship whose chance of success is P per cent.
b) To send two ships, each of whose chance of success is P/2 per cent. At least one ship needs to be successful for the mission to be a success.
Which is your best option?
2. The two oracles
Before you are two oracles, Randie and Rando, who will answer yes or no to any question you ask.
Randie answers yes or no at random to all questions.
Rando decides at random whether to tell the truth or to lie for each question, and then answers the question accordingly.
Is there a way to tell them apart? If so, what is it?
3. Bad maths
Johnny’s homework is to calculate 5548-5489. The answer is 59. He figured that the 548 cancelled out, leaving 59.
He tested the technique again. He typed in a subtraction of the form XXYZ – XYZW where X, Y, Z and W were distinct digits, and found out it was indeed XW!
How many of the digits in the new calculation are the same as the digits in the old one? (i.e does X = 5, Y = 4, Z = 8 or W = 9)
I’ll be back at 5pm UK with solutions.
PLEASE NO SPOILERS
Mathematical Puzzles and Curiosities by Ivo David, Tanya Khovanova and Yogev Shpilman is published by World Scientific. I have edited the wording of the three puzzles to make them fit the column.
I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
