This week’s Puzzle Corner is a collection of puzzles dealing with letters of the alphabet. While they are not necessarily mathematical in nature (although one could argue this point), these puzzles have a place in a well-rounded mathematics curriculum.

Alphabetical Puzzlers is a collection of four puzzles that use letters of the alphabet in a puzzling (please forgive the pun) manner. The first two puzzles are similar; solving one should help students solve the other. Both of these puzzles have two lists, with each of the letters from a to w placed into one or the other of these lists according to a certain rule. Students are challenged to discover that rule. They are then challenged to determine into which lists the x, y, and z should be placed.

The last two puzzles are also similar. Once one of them is solved (which may take some time), the other solution should quickly follow. Both these puzzles consist of a list of letters in a series with the last three letters missing. Students are challenged to determine the next letters in each series.

These puzzles, especially the last two, may prove to be frustrating for many students since their solutions require divergent thinking. Once each puzzles’ secret is uncovered, students may wonder why they didn’t come up with the solution much sooner.

One of the goals of this activity is to give students an opportunity to think divergently. Another goal is to build students’ persistence in problem-solving. These goals are not well served if the first student to solve the puzzle blurts out the answer, robbing the other students of the chance to discover their own solutions. To prevent this from happening, caution students not to give away the answers. Explain that there will be a time later in the week when those who have solved the puzzles can share their answers. That said, we hope that you find these puzzles both challenging and enjoyable.

## Activity Page

**Puzzle #1:** Each of the lists below groups letters according to a certain rule. Your challenge is to find that rule and use it to determine where the X, Y, and Z would go.

List #1: A E F H I K L M N T V W

List #2: B C D G J O P Q R S U

**Puzzle #2:** Each of the lists below groups letters according to a certain rule. Your challenge is to find that rule and use it to determine where the x, y, and z would go.

List #1: a c e m n o r s u v w

List #2: b d f g h i j k l p q t

**Puzzle #3:** What letters come next in this sequence?

O, T, T, F, F, S, S, E, ___, ___, ___

Puzzle #4: What letters come next in this sequence?

J, F, M, A, M, J, J, A, S, ___, ___, ___

**Solutions**

Click the arrow below to view the solutions.

**Puzzle #1**: Each of the lists below groups letters according to a certain rule. Your challenge was to find that rule and use it to determine where the X, Y, and Z would go.

List #1: A E F H I K L M N T V W

List #2: B C D G J O P Q R S U

Solution: X, Y, and Z would go in List #1 since all the letters in that list consist of straight lines.

**Puzzle #2**: Each of the lists below groups letters according to a certain rule. Your challenge was to find that rule and use it to determine where the x, y, and z would go.

List #1: a c e m n o r s u v w

List #2: b d f g h i j k l p q t

Solution: x and z would go in List #1 because they are “short” letters. y would go in List #2 because it is a “long” letter.

**Puzzle #3**: What letters come next in this sequence?

O, T, T, F, F, S, S, E, __, ___, ___

Solution: The next three letters are N, T, E (nine, ten, eleven).

**Puzzle#4**: What letters come next in this sequence?

J, F, M, A, M ,J ,J ,A, S, ___, ___, ___

Solution: The next three letters are O, N, D (October, November, December).