Imagine you’re a detective on the hunt for a mysterious creature causing chaos in your town. After months of investigation, you’ve narrowed down the suspects to five people: the mayor, the tailor, the baker, the grocer, and the carpenter. To find out who the creature is, you’ve invited them all to dinner with a clever plan. You have a rare antidote that can reveal the creature, but there’s a problem. Your pet goat ate most of it, leaving you with just one 50-gram square. The antidote needs to be divided into 10-gram portions to work, so you need to split the square into five equal parts.
To divide the antidote precisely, you have a laser-cutting tool. This tool can make exact cuts, which is important because other methods aren’t accurate enough. You can choose from 8 points on the square to start and end each cut. The laser will make all the cuts at once, and you can cut the square into as many pieces as needed, as long as you can group them into 10-gram portions. Remember, you can’t fold or change the square in any other way, and you only have one chance to use the laser cutter.
The full moon is rising, and time is running out. If you don’t divide the antidote correctly, someone will transform into the creature. How can you cut the antidote into perfect fifths to save everyone? Take a moment to think about it.
When faced with puzzles like this, it can be helpful to experiment. Try cutting a piece of paper to see what shapes you can create. If you cut the square into quarters, you’ll get four pieces, but you need five. Maybe you can trim a bit off one of the quarters to make a fifth.
At first, cutting one section seems promising, but the last cut leaves you with a piece that’s too small. What if you start with a different section? That might give you a quarter, but can you trim it just right?
With one more cut, you might notice something interesting. The cuts create several triangles and a square in the middle. The pieces from each triangle can be rearranged to form a square identical to the middle one. This means you’ve successfully divided the antidote into perfect fifths!
Once you’ve divided the antidote, you secretly give each suspect a dose just as the full moon appears. A transformation begins, but then it suddenly stops. Your precise measurements worked, and the townspeople and animals are safe once again.
This type of problem shows that while you can solve it using geometry, experimenting can often lead you to the solution more easily. By trying different approaches, you can discover new ways to solve puzzles and challenges.
Try cutting a piece of paper into five equal parts. Use scissors and see if you can create five identical shapes. This will help you understand the challenge of dividing the antidote into equal portions.
Using a ruler and pencil, draw a square on graph paper. Plan and draw lines to divide the square into five equal areas. Share your solution with classmates and discuss different strategies.
In groups, role-play as detectives and suspects. Create clues and solve riddles to identify the werewolf. This will enhance your problem-solving and teamwork skills.
Create a piece of art using geometric shapes. Use the concept of dividing a square into equal parts to design a pattern. This activity combines creativity with mathematical precision.
Write a short story about a detective solving a mystery using math and logic. Include how they overcome challenges and use clever strategies to find the solution.
You’re on the trail of a creature that’s been causing trouble in your town. After months of detective work, you’ve narrowed your suspects to five individuals: the mayor, the tailor, the baker, the grocer, or the carpenter. You’ve invited them to dinner with a simple plan: you’ll slip a square of a rare antidote into each of their meals. Unfortunately, your pet goat just ate four of the squares, and you only have one left. Luckily, the remaining square is 50 grams, and the minimum effective dose is 10 grams. If you can precisely divide the square into fifths, you’ll have just enough antidote for everyone.
You’ll need to use a laser-cutting tool to cut the square; every other means available to you isn’t precise enough. There are 8 points that can act as starting or ending points for each cut. To use the device, you’ll have to input pairs of points that tell the laser where to begin and end each cut, and then the laser executes all the cuts simultaneously. It’s okay to cut the square into as many pieces as you want, as long as you can group them into 10-gram portions. However, you can’t fold the square or alter it otherwise, and you only get one shot at using the laser cutter.
The full moon is rising, and in a moment, someone will transform unless you can cure them first. How can you divide the antidote into perfect fifths, cure the secret creature, and save everyone? Pause the video now if you want to figure it out for yourself.
When it comes to puzzles that involve cutting and rearranging, it’s often helpful to actually take a piece of paper and try cutting it up to see what you can get. If we cut certain points, we’d get fourths, but we need fifths. Maybe there’s a way to shave a bit off of a quarter to get exactly one fifth.
Cutting one section looks good at first, but that last cut takes off a quarter of a quarter, leaving us with a portion that isn’t enough to cure the creature. What if we started with a different section instead? That would also give us a quarter. And is there a way to shave just a bit more off?
If we make one more cut, we may start to notice something. With these cuts, we’ve got several triangles and a square in the middle. But the pieces that make each triangle can also be rearranged to make a square identical to the middle one. This means that we’ve split the antidote into perfect fifths!
What’s interesting about this sort of problem is that while it’s possible to solve it by starting from the geometry, it’s actually easier to start experimenting and see where that gets you.
You secretly dose each of the townspeople as the full moon emerges in the sky. And just as you do, a transformation begins. Then, just as suddenly, it reverses. Your measurements were perfect, and the people and animals of the town can rest a little easier.
Geometry – The branch of mathematics that deals with points, lines, shapes, and spaces. – In geometry class, we learned how to calculate the area of different shapes.
Square – A four-sided polygon with equal sides and four right angles. – The teacher asked us to find the perimeter of a square with sides measuring 5 cm each.
Triangle – A three-sided polygon. – We used a protractor to measure the angles of the triangle to ensure they added up to 180 degrees.
Portion – A part or fraction of a whole. – We shaded a portion of the circle to represent one-third of the total area.
Cut – To divide a shape into parts using a line or plane. – The problem asked us to cut the rectangle into two equal triangles.
Equal – Having the same value, measure, or quantity. – The two angles were equal, each measuring 45 degrees.
Shape – The form or outline of an object. – We identified the shape as a hexagon because it had six sides.
Experiment – A test or investigation, especially one planned to provide evidence for or against a hypothesis. – In our experiment, we measured how the area of a circle changes as the radius increases.
Measurement – The size, length, or amount of something, typically determined by comparing it to a standard. – Accurate measurement of the angles was crucial for solving the geometry problem.
Fifths – Dividing something into five equal parts. – We divided the line segment into fifths to find the exact location of each point.
