Letter Groupings

The letters of the (English) alphabet can be grouped into four distinct categories.

A M

B C D E K

F G J L

H I

Based on the categories established by the first 13 letters, can you place each of the remaining 13 letters in the correct group?

This question is tricky because it's not about the sounds the letters make, or the frequency of letters, but about the shapes of the (capital) letters.

The categories are:

A M T U V W Y (left-right mirror images)

B C D E K (top-bottom mirror images)

F G J L N P Q R S Z (no symmetry)

H I O X (symmetry about both axes)

Number Words

In the solution to A Unique Number, I asked a bonus question. "Can you think of a number whose letters when spelled out in English are all in alphabetical order?" Several people replied via Twitter with the correct answer of "forty." You may have found a shortcut to the solution if you noted that none of the single-digit numbers have their letters in alphabetical order, nor does the word "teen." This allows you to skip ahead to 20, 30, etc. Can you use a similar strategy to answer the following questions?

• What is the lowest number that requires the five vowels A, E, I, O, and U only once each in its spelling?
• What is the lowest number that requires the six letters A, E, I, O, U, and Y only once each in its spelling?

Click below to see the answers.

The lowest number that requires the five vowels A, E, I, O, and U once each in its spelling is 206 (two-hundred and six).

The lowest number that requires the six letters A, E, I, O, U, and Y once each in its spelling is 230 (two-hundred and thirty).

The strategy to quickly find these answers is to note which vowels are used in the base numbers, one, two, three, etc, then avoid combinations that include multiples of the same vowel. For example, you can skip past the 100s entirely, because "one-hundred" contains two of the letter "e".

The Nine Dot Puzzle

The following is a classic "thinking outside the box" puzzle. Can you connect all nine dots below by drawing exactly four straight lines, without lifting your pencil or tracing back over any line?

Give it a try before you click below for the answer.

If this puzzle looks familiar, it's because it dates back at least as far as Sam Loyd's 1914 Cyclopedia of Puzzles. When I said this was a classic "thinking outside the box" puzzle, that was a clue. You have to think outside the bounds of the box created by the nine dots to come up with a solution.

Apples and Oranges

You work in a factory boxing fruit. In front of you are three boxes labeled "apples," "oranges," and "apples & oranges." One box contains only apples, one contains only oranges, and one contains a mixture of both apples and oranges. Unfortunately, the label machine has gone haywire and has mislabeled all three boxes. Can you look at one piece of fruit from only one of the boxes and correctly label all three? Click below for the solution.

The key to this puzzle is that the type of fruit you pull from the box is not the only piece of information you have to work with. You also have the three labels that you know are incorrect. Pull a piece of fruit from the box labeled "apples & oranges." If it is an apple, then you know that this is the apples-only box. That means that the box (incorrectly) labeled "oranges" must be the box with both apples and oranges, and the box labeled "apples" must contain only oranges.

(It's interesting to note that if you pick from either the box labeled "apples" or the box labeled "oranges," you can't figure out the composition of the box. Only selecting from the box labeled "apples & oranges" leads to a solution.)