earlier today These puzzles have been put forward by the Oxford University Department of Physics.
1. Cup puzzle
You are in a hurry to work. You pour yourself a cup of black coffee, but it is very hot. You intend to add a steady amount of cold milk to it, but you know that even after that, the coffee will need to cool down for a few minutes before you can drink it.
In this case the coffee cools more:

1) Add milk immediately, then wait a few minutes before drinking.

2) Wait a few minutes and then add the milk just before drinking.
solution 2) Wait a few minutes and then add the milk just before drinking.
In case 2) the liquid in the cup is initially hotter than in case 1) when milk is added. Hotter things cool faster than less hot things because there is a greater difference in temperature with the surrounding environment. So the cooling rate will be greater in case 2). Since in both cases, the liquid is simultaneously cooling at different rates, the liquid that spends the most time cooling at a faster rate will eventually be cooler, once the milk is added.
2. Fly away
A fly fell to the bottom of a glass on a very sensitive digital scale. Suddenly the fly takes off. What happens to the readings on the scale?

1) rise

2) go down
solution: Both! First it goes up, then it goes down.
Imagine you are standing on your bathroom scale. In order to jump off the scale, you will hit the scale, which will register a heavier weight. The situation with the fly is similar. Its wings push the air down, which in turn pushes the bottom of the glass. But when it is high enough that air movement does not reach the bottom of the glass, the measured weight will be the weight of the empty glass.
3. Bonded balls
A weightless thread connects two identical metal balls. The middle of the thread is located above the edge of the table. I left both balls at the same time. What happens sooner: Ball 1 flies off the table or Ball 2 hits its side?
solution Ball 1 flies off the table
The tensile strength of the thread is the same on both sides. But the horizontal component of this force is greater for ball 1 than for ball 2. so ball 1 will accelerate in the horizontal direction faster and take less time to travel the same horizontal distance.
4. Breaking fun
Proof (1/2) x (3/4) x … x (99/100) <1/10
It sounds complicated, but there is a twoline solution.
solution
Let’s say (1/2) x (3/4) x … x (99/100) = A.
Then 101 A = (3/2) x (5/4) x … x (101/100), and 1 / A = (2/1) x (4/3) x… x (100/99) . 101A and 1/A each contain fifty fractions in brackets, and each fraction in 101A is less than the corresponding fraction in 1/A. Thus 101a < 1/a. The rest follows:
a^{2} <1/101 <1/100. Thus a <1/10
I explained the solution to more than two lines. In terms of the actual mathematical detection, all you need are two lines.
Thanks to Professor Alexander Lvovsky at Oxford University for these puzzles. Professor Lvovsky runs Oxford Comprehensive School of Mathematics and Physics Online (COMPOS)a new initiative that teaches mathematics and physics to sixth graders from UK public schools at a level deeper than Alevel curricula.
The course is free and anyone 12 or 13 years old is eligible. There are still places to eat for this year, so please pass the word around!
I will be back with new puzzles in a couple of weeks.
I post a puzzle here every two weeks on Mondays. I am always looking for great puzzles. If you would like one suggestion, send me an email.
I am the author of several math and puzzle books, as well as the coauthor with Ben Lyttleton of the Football School children’s book series. The latest football school series is Greatest quiz book everOutside now!
I give school lectures on math and puzzles (online and in person). If your school is interested please contact us