The names of the 50 United States contain 25 different letters of the alphabet, a ratio of 2-to-1. (You could get the missing letter *q* by including the Canadian province of Quebec, but we aren’t going there.) Here is a challenge to see how many state names you can spell using only a limited number of letters of the alphabet.

1. Which state name uses only three different letters?

2. Adjoin two more letters to those three, and spell two more state names—a total of three states using only five different letters.

3. Adjoin two more letters (a total of seven letters) to spell two more states (a total of five states).

4. Adjoin three more letters to add three more states (a total of eight states using 10 letters).

5. Adjoin three more letters for four more states (naming 12 states with 13 different letters).

6. Adjoin one more letter to name three more states. (You now have more states than letters: 15 states using 14 letters.)

7. Adjoin only one more letter to add four more states (for a total of 19 states using 15 letters).

8. Adjoin two more letters to name seven more states (for a total of 26 states using 17 different letters).

9. Adjoin the 18th letter to add seven more states (for a total of 33 states).

10. Adjoin the 19th letter to name four more states (for 37 states in all).

11. Adjoin one more letter to add four more states. (If you have managed to complete each step successfully, you now have 41 states using 20 different letters, a ratio of better than 2-to-1.)

12. What five letters (besides *q*) have you not yet used, and which nine states have not yet been spelled?

Extra credit:

How can you spell the names of 42 different states, still using only 20 different letters?

There is an alternate solution to the puzzle as presented that ends up with the same number of states, and has at least as many spelled after each step, but has many more after some steps.

The first difference is at step 5, where c,f,r are adjoined, adding 5 states: Arkansas, California, Colorado, Florida, Wisconsin for a total of 13

Step 6. Adjoin t, adding two states: North Carolina, North Dakota for a total of 15.

Step 7. Adjoin u, adding 4 states: Louisiana, South Carolina, South Dakota, Utah for a total of 19.

Step 8. Adjoin e, m, adding Connecticut, Delaware, Maine, Massachusetts, Missouri, Montana, Minnesota, Oklahoma, Rhode Island, Tennessee for a total of 29.

Step 9. Adjoin g, adding Georgia, Michigan, Oregon, Washington for a total of 33.

Step 10. Adjoin v, adding Nevada, Vermont, Virginia, West Virginia for a total of 37.

Step 11. Adjoin y, adding Kentucky, Maryland, New York, Wyoming for a total of 41.

The unused letters are b,j,p,x,z. The 9 states not yet spelled are Alabama, Arizona, Mississippi, Nebraska, New Hampshire, New Mexico, New Jersey, Pennsylvania, Texas.