Challenges cover a variety of topics
You will need serious matrix solving skills to solve today’s challenge.
Todays challenge is strait forward: solve the Machiavellian Matrix. Machiavellian means crafty and duplicitous, like a trickster. Sometimes this means breaking the rules or finding loopholes. With matrices, machiavellian often means horrifying. Variables are x, y, and z, sum on the right.
\left(\begin{matrix} xyz & xyz & xyz & xyz \\ x & y & z & 1 \\ 4 & 1 & 1 & 0 \end{matrix}\right)You will need matrices and combinatorics to solve this challenge.
In a city with infinite people, there are only three types of pets. They are dogs, cats, and fish. 60% of people have a pet. The ratio of dogs to cats is 2:3, and the ratio of poeple with cats to those with fish is 5:6. All pets are randomly distributed. The challenge is to find what fraction of the people own dogs.
Today’s challenge requires matrices.
A mixture is made by mixing 3 powders: powders 1, 2, and 3. The powders are each made from different amounts of the same 3 ingredients. The ingredients are named A, B, and C. Powder ratio’s are A : B : C. Powder 1 is 1 : 1 : 2 and weighs 35 g/cm3, powder 2 is 5 : 2 : 3 and weighs 44 g/cm3, and powder 3 is 4 : 15 : 1 and weighs 43 g/cm3. The mystery mixture is 2 : 2 : 3. The challenge is: how much of each powder is in the mixture, and how much does the mixture weigh per cm3? Answer in 1 : 2 : 3 and g/cm3.