I would greatly appreciate an explanation of the solution. I don’t understand the explanation in the book (pg. 101). Thanks!

City A City B City C City D City E City F
City A
City B
City C
City D
City E
City F

In the table above, what is the least number of table entries that are needed to show the mileage between each city and each of the other five cities?
a) 15 - correct
b) 1
c) 5
d) 0
e) 6

Think of it as a 6x6 table (Total 36 distances). Now the distance from a city to itself is 0 so we lose 6 distances leaving only 30 spaces to fill. If you actually fill the table, Distance from City A to City B is the same as that from City B to A and so on for all the other cities. (If you fill in arbitrary variables for the distances you will notice that the table is symmetrical bout the diagonal). So the minimum number of distances you will need will be (30)/2 = 15. Which is the answer.

Great explanation, NO0v1907. gphil, take NO0v1907's suggestion and actually fill the thing in so you can see how it works. Then use that to understand the pattern described so that you don't actually have to fill it all in next time you see something like this.