1, cattle grazing problem.
There are three pastures where the grass grows dense and fast. Their areas are 10 to 3 mu, 10 mu and 24 mu respectively. The first pasture can feed 12 cows for 4 weeks, and the second pasture can feed 2 1 cow for 9 weeks. If the third ranch is to keep 18 weeks, how many cows will this ranch keep? There are many solutions to this problem, but Newton especially likes his arithmetic solution.
2. Tigers and foxes.
A tiger found a fox at a distance of 10 meters, and immediately jumped on it. The tiger runs 7 steps, and the fox runs 1 1 step, but the frequency of the fox is fast. Tigers can run three steps, and foxes can run four. Can the tiger catch up with the fox? How many meters will the tiger run if it can catch up? The tiger can catch up with the fox when it runs 66 meters. Interestingly, we don't know the speed of tigers and foxes, but we can get the answer to the question.
3. Fractal and dragon.
There are two types of fractal, one is geometric fractal and the other is random fractal. A straight line is one-dimensional, a square is two-dimensional, a cylinder is three-dimensional, and the fractal dimension is a fraction. Starting from an isosceles right triangle, make an isosceles right triangle with the right side of the isosceles right triangle as the hypotenuse, and remove the hypotenuse of the original right triangle.
Then take the right side of the new isosceles right triangle as the hypotenuse, make other isosceles right triangles, and remove the original hypotenuse. If you go on like this, you will get a dragon.