This week’s puzzle was based on a game that was originally described in the "Mathematical Games" section of Scientific American, April, 1969 by Anatol W Holt.
Two players each think of a Target Word containing the agreed number of letters. It’s best to start with three-letter words, and increase the length as the players improve. Each player in turn suggests a Probe Word, and receives a reply of Odd or Even. This response indicates the number of correct letters in the correct place in the Probe Word, with zero being even. The first player to find their opponent’s Target Word is the winner.
This is quite a fun game to play in its own right, and it bears a certain resemblance to a board game called Mastermind, sold by Hasbro. This in turn also resembles an old pen-and-paper game called Bulls and Cows.
All three of these games have been implemented on various computers, phones and tablets, and I’m sure that some of our readers will be thinking of writing a program for one of the games.
The puzzle was to determine the Target Word from the six Probe Words and Responses below. It can be solved by trial and error (or by writing a program), but the challenge here is to deduce the word logically. From the information given you can work through problem and find the solution.
DAY – Even
MAY – Even
BUY – Even
SAY – Odd
DUE – Odd
TEN – Odd
From DAY and MAY being even we can deduce that the first letter is neither D nor M. With the same “polarity” and the AYs being the same, D and M have to be both right (impossible) or both wrong.
From DAY (or MAY) and SAY having different polarity, and knowing that D (or M) is wrong, S must be the first letter.
Both MAY and BUY are wrong in the first letter, have the same third letter, and the same polarity. So neither A nor U is the second letter.
As D isn’t the first letter and U isn’t the second letter, DUE being odd shows that the final letter is E.
Finally, as T isn’t the first letter and N isn’t the third letter, TEN being odd shows the second letter is also E.
This gives SEE as the word.