## Two Is Company, Three Is A Crowd

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Two Is Company, Three Is A Crowd

# Two Is Company, Three Is A Crowd

## Two Is Company, Three Is A Crowd

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On-air challenge: Given three three-letter words, give a three-letter word that can follow each to complete a familiar six-letter word. None of the words in a set will be related in meaning. For example, given "dam," "man" and "sew," the answer would be "age," which results in "damage," "manage" and "sewage."

Last week's challenge from Sam Loyd: This challenge appeared in a puzzle column in the Woman's Home Companion in January 1913. Draw a square that is four boxes by four boxes per side, containing altogether 16 small boxes and 18 lines (across, down and diagonal). There are 10 ways to have four boxes in a line — four horizontal rows, four vertical columns, plus the two long diagonals. There are also eight other shorter diagonals of two or three squares each. The object is to place markers in 10 of the boxes so that as many of the lines as possible have either two or four markers. What is the maximum number of lines that can have either two or four markers, and how do you do it?

Answer: It is possible for 16 lines to have either two or four markers. Sam Loyd's arrangement includes the first and third boxes of the top row, the seventh and eighth boxes of the second row, all four boxes of the third row, and the 14th and 15th boxes of the bottom row. Any rotation of this answer also works.