A mother has 4 children. On Halloween, she decides to give them 200 candies one by one, starting with the youngest child, then the second youngest, third youngest, etc. At some point, they have to interrupt the procedure and eat dinner, but when they continue, nobody remembers which was the last child to get a candy. How can the mother distribute the remaining candies to the kids without starting over again or counting how many candies have been given so far?
SOLUTION
The mother can start giving the remaining candies one by one in the reverse order, starting with the oldest child, then the second oldest, etc.
When a car is making a turn, are its front wheels parallel to each other?
SOLUTION
The front wheels are not parallel to each other. The reason is that when steering, all wheels are turning along arks that have a common center. Otherwise, the car would be drifting.
You had 10kg of cucumbers, each of which consisted of 99% water. After leaving them in the sun, some of the water in the cucumbers evaporated. If the cucumbers ended up with 98% water in them, how much of their weight did they lose?
SOLUTION
The cucumbers lost half of their weight.
If the water was 99% of the total weight, the remaining substance must have weighed 0.1kg. If after the evaporation the substance comprises 2% = 1/50 of the cucumbers, the total weight must be 50 x 0.1kg = 5kg.
Can you draw a 3-dimensional object which looks like a square when looked from one side, a triangle when looked from a second side, and a circle when looked from a third side?
Help Finn find the way to the secret cave through this hedge maze. Additionally, try to spot two tiny soldiers with large hats, a platypus pair, and a present.
Monday, six friends went camping. Tuesday, John, Jack, and James cooked some mushrooms. Wednesday came and they ate the mushrooms. Thursday found them dead. Exactly one friend survived, how come?
SOLUTION
The six friends are called John, Jack, James, Tuesday, Wednesday, and Thursday. John, Jack, James, and Tuesday cooked the mushrooms. Wednesday joined them and they ate the mushrooms. Thursday was the one to find them dead, so he is the survivor.
Mathematical Puzzles: A Connoisseur’s Collection by Peter Winkler is not your casual puzzle book. Even though most of the problems inside are easy to formulate, many of them require extensive mathematical background and well-developed analytical thinking. If you possess these two qualities, however, you will certainly enjoy this book. The puzzles are hard, the solutions are beautiful, and the explanations are very well-written. The book contains over 100 puzzles that are split into different categories – Insight, Numbers, Geometry, Geography, Algorithms, and others. In order to give you an idea of what to expect, I have selected several puzzles from the book which represent its overall level.
1. Given 10 red points and 10 blue points on the plane, no three on a line, prove that there is a matching between them so that line segments from each red point to its corresponding blue point do not cross.
2. A phone call is made from an East Coast state to a West Coast state, and it’s the same time of day at both ends. How can this be?
3. The hour and minute hands of a clock are indistinguishable. How many moments are there in a day when it is not possible to tell from this clock what the time is?
4. Associated with each face of a solid convex polyhedron is a bug that crawls along the perimeter of the face, at varying speed, but only in the clockwise direction. Prove that no schedule will permit all the bugs to circumnavigate their faces and return to their initial positions without incurring a collision.
MP:ACC is one of the most valuable puzzle books in my collection. If you are up to the challenge it offers, you owe yourself a favor to buy it. Even if you don’t feel too confident in your abilities to solve the problems in the book, you can still get it and study the solutions. And if you need more mathematical brilliance, you can check out Peter Winkler’s other puzzle book, Mathematical Mindbenders.
You are shown two cylinders – one of them is made of gold and hollow, the other one is made of alloy and solid. Both of them have the same weight, shape, and are colored in black. How can you figure out which cylinder is the golden one, without scratching the paint?
SOLUTION
Simply roll the two cylinders on the ground. The hollow one will roll farther than the solid one since it will have a higher moment of inertia.
