Is there one mineral that you can identify as the softest?
B
b
Is there a test you can do to determine which mineral is the hardest? What possible outcomes are there of this test?
A
a
Mineral C: Talc
Mineral A: Not Fluorite Mineral B: Not Gypsum Reasoning: See solution.
B
b
See solution.
Practice makes perfect
a
From the given information, we know that C is scratched by the other three minerals. Therefore C has to be the softest mineral, which is talc.
Since A is scratched by B, we know that A cannot be the hardest mineral. Conversely, it must also mean that B cannot be the second softest mineral.
b
We know that B is either the hardest or the second hardest. Therefore, the first test we should do is scratching D with B. There are two possible outcomes of this test.
D scratches B
If D scratches B, we know that D is the hardest, B is the second hardest and A is the second softest.
B scratches D
If B scratches D, then B is the hardest. In this case, we need one more test to determine which is the second hardest of D and A. Therefore, we have two possible outcomes.
