Brainteaser # 5
__If there are two cups in front of two cups, two cups behind two cups, and two cups in between two cups, what’s the fewest number of cups you need to solve the puzzle?
National Mathematics Day Friday 18 May is National Mathematics Day. This year marks one century since Alan Turing’s birth. Alan was a mathematician well known for his efforts cracking codes during the Second World War. To celebrate, AAMT will be releasing several activities about codes and code breaking. Need more codes? Maths and Stats by Email has code activities too! The World Education Games Congratulations to 4R for getting the highest score for our school in the World Maths Day Education Games! Big congratulations to the top 3 students; Molly Ryan Hannah Sully Henrietta Wilson
| Brainteaser #4 Answer
If the class takes one of the chains, and cuts all of the links in that chain they then have three open links and four chains. They can then use the three open links to join the four chains into one long chain. Will appear one week after the brainteaser has been posted. Don't forget to explain how you got your answer. What did you think? How could you prove your answer is right? |
_Do Sharks Do Maths?
Imagine you’re a shark, swimming around in the ocean, looking for a meal. There’s nothing edible in sight – so where do you swim to find food?
Your first thought might be to swim back and forth in long straight rows, like you are mowing the lawn. You could search one area of the ocean and then move on to another. However, this strategy might not be the best way to find a meal – if you’re swimming in an obvious pattern, other animals might be able to predict it and stay out of your way.
Another option would be to go on a random swim – in mathematics we call this a random walk. You could pick a direction at random, swim for a bit, and then pick another direction, swim for a bit, and so on. This sort of behaviour is impossible to predict, giving you a much better chance to catch a meal.
Unfortunately, this has a different problem – most random walks tend to stay around in the same area for a long time. You might be really good at catching all the food in the neighbourhood, but once you’ve eaten all the fish nearby, you’re going to get really hungry.
What you really want is a way to swim unpredictably while covering a large area. Researchers theorised that in an ocean with few fish to eat, the best strategy would be to swim randomly, occasionally swimming for a longer distance in one direction. Called a Levy walk, this would move you away from a single spot.
Recently, scientists from Australia and around the world tagged several species of predatory fish, including sharks and tuna. They found that in many environments, fish often used Levy walks to find their prey. However, in some areas they still tended to use regular random walks. In a few examples, the scientists couldn’t work out any patterns to the fish’s movement.
More information
Imagine you’re a shark, swimming around in the ocean, looking for a meal. There’s nothing edible in sight – so where do you swim to find food?
Your first thought might be to swim back and forth in long straight rows, like you are mowing the lawn. You could search one area of the ocean and then move on to another. However, this strategy might not be the best way to find a meal – if you’re swimming in an obvious pattern, other animals might be able to predict it and stay out of your way.
Another option would be to go on a random swim – in mathematics we call this a random walk. You could pick a direction at random, swim for a bit, and then pick another direction, swim for a bit, and so on. This sort of behaviour is impossible to predict, giving you a much better chance to catch a meal.
Unfortunately, this has a different problem – most random walks tend to stay around in the same area for a long time. You might be really good at catching all the food in the neighbourhood, but once you’ve eaten all the fish nearby, you’re going to get really hungry.
What you really want is a way to swim unpredictably while covering a large area. Researchers theorised that in an ocean with few fish to eat, the best strategy would be to swim randomly, occasionally swimming for a longer distance in one direction. Called a Levy walk, this would move you away from a single spot.
Recently, scientists from Australia and around the world tagged several species of predatory fish, including sharks and tuna. They found that in many environments, fish often used Levy walks to find their prey. However, in some areas they still tended to use regular random walks. In a few examples, the scientists couldn’t work out any patterns to the fish’s movement.
More information
Maths games and videos
Check out these great games and videos for your selected year level. If you need extra practise with a particular area of Maths you will find it under the subject heading.
Have fun!
https://www.mathgametime.com
Read maths!
What’s the best strategy to use when playing hangman?
Do maths!
A grocery store is running a competition. Can you work out the maths required to understand what’s going on?
See maths!
Mathematicians often draw diagrams on blackboards to help them with their work. Here is a collection of really cool blackboard diagrams.
Have fun!
https://www.mathgametime.com
Read maths!
What’s the best strategy to use when playing hangman?
Do maths!
A grocery store is running a competition. Can you work out the maths required to understand what’s going on?
See maths!
Mathematicians often draw diagrams on blackboards to help them with their work. Here is a collection of really cool blackboard diagrams.