Golomb's Gambits: Name that state

The following puzzle first appeared in February 1998.

All these problems involve the names of states of the Union. See how many you can solve with-out consulting an atlas.

1. Find a set of only six letters that can be used (allowing repetition) to spell the names of four different states.

2. Which state has four different repeated letters?

3. What letter occurs most frequently as the last letter of the name of a state? What letter comes in second?

4. What two letters occur most frequently as the first letter of the name of a state?

5. For each state, consider the ratio of the total number of letters divided by the number of distinct letters. (Example: Illinois—eight total, five distinct, ratio of 8/5 = 1.6.) For which state is the ratio maximized?

[Solutions below]



1. The set [A,D,H,I,O,W] allows us to form Hawaii, Idaho, Iowa, Ohio.

2. North Carolina has two each of A, N, O, and R.

3. Twenty-one of the 50 states have names that end in A. Far behind in second is S, which ends five state names. Tied for third are E, N, and O with four each.

4. M and N each begin eight state names. All eight of the M states have one-word names, while six N states have two-word names.

5. The ratio is maximized for Mississippi, which it is 11/4 = 2.75.