When put into test tubes in the lab, the four species of borjums always arrange themselves in groups of four, according to their weight, with the lightest on top and heaviest on the bottom. It is impossible to see more than two of them at a time, or to determine whether the two are next to each other or are separated by one or more borjums of intermediate weight. (A strange organism, no?) However, six definite facts have been established by the biology students to date, as follows:
- The alpha borjums are always lower down than the betas.
- The gammas are always higher up than the alphas.
- The delta borjums are always lower down than the gammas.
- The betas are always higher up than the deltas.
- The deltas are always lower down than the alphas.
- The gammas are always higher up than the betas.
Write the relative positions of the four species. Also, which of the six facts didn’t you need?
a = alpha, b = beta, g = gamma, d = delta
| 1: | b | 2: | g | 3: | g | 4: | b | 5: | a | 6: | g | |||||
| a | a | d | d | d | b |
All of this shakes out into this:
g
b
a
d
b
a
d
Statements 1, 4, 5, and 6 are sufficient to figure this out.