The rules are simple: you want to place the sheep on the board so that the wolves can’t eat them. A wolf can eat a sheep if it has a direct path to it – or is in same row, column, or diagonal as that sheep. Can you place all your wolves and sheep on an nxn grid so all the sheep are safe?
Supporting Material: Virtual Tools
Is it possible to measure all possible integer lengths on a ruler without marking every integer on that ruler? This is an engaging and challenging problem for all. Beautiful mathematics can be revealed while delving deeper into this seemingly easy question.
Place our numbers into the cauldrons in ascending order – you can choose which cauldron each one goes in. However, if two numbers in one cauldron add up to a third number in that same cauldron, they bubble up and cause an explosion! This means that all the numbers, leave the cauldrons, and you must start all over again.
Our goal is to find the largest number we can place in our cauldrons without them exploding… do you think you’re up for this daunting task?
A town faces an epidemic of zombies! Luckily, the virus has just started to spread and the infected are able to stave off their hunger for human brains… for now. In fact, they’re willing to work alongside the remaining humans to help them get across a river to safety. Can you get all the humans and zombies across safely?
Skyscrapers come in so many different sizes! Sometimes you can’t see small skyscrapers if tall ones are in front of them. Using clues about how many skyscrapers you can see from each side you look at them, can you figure out the layout of the entire city?
SET is a fun game that can be enjoyed by kids as young as 6 and is challenging even for adults. It is rich in counting problems and is great for getting people to pose problems. It is also an example of a finite geometry and interesting to explore how well one’s geometric intuition works.
Triangles and Squares live together in neighborhoods. However, the Polygons all believe two things: “I am unhappy if fewer than 1/3 of my immediate neighbors are like me.” and “I am unhappy if I have no immediate neighbors.”
Merriam Webster defines gerrymandering as “the practice of dividing or arranging a territorial unit into election districts in a way that gives one political party an unfair advantage in elections.” This activity tries to make sense of that definition using a few examples.