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  Number & Math Play

Puzzle about Puzzles
Q Ann, a very competitive person, decides to give herself 2 points for every crossword puzzle in her daily newspaper that she completes correctly and to forfeit 3 points for every crossword in the paper that she completes incorrectly or cannot complete.

After 30 days of working the puzzles, Ann has a score of zero. How many puzzles has she solved correctly?

A Ann solved 18 puzzles correctly; therefore, at 2 points a puzzle, she earned 36 points. But Ann failed to solve 12 correctly; therefore, at 3 points a puzzle, she lost 36 points.

In order to arrive at a total of 0 points, the total points for correctly and incorrectly solved puzzles must be equal. Since Ann loses more points for an incorrect puzzle than she gains for a correct one, you know she has to solve more correctly than incorrectly. That means she has to have more than 15 correct puzzles and less than 15 incorrect ones, since the total number of puzzles is 30.

Try out 16 correct (gain 32 points) and 14 incorrect (lose 42 points). That's wrong because it would leave Ann with -10 points. Try 17 correct (gain 34 points) and 13 incorrect (lose 39 points). It still doesn't come out even. Try 18 correct (gain 36 points) and 12 incorrect (lose 36 points). Bingo!

Source: Carter & Russell,Classic Brain Teasers,p.53